Lower Moreland Township School District / Overview



Study Island

Copyright © 2013 Study Island - All rights reserved.

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Generation Date: 01/18/2013

Generated By: Erica Ginnetti

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Cumulative Frequency Plots

1. A contractor designed and built a subdivision. It took 6 months for the new subdivision to reach 100 percent occupancy. The following cumulative percentage plot shows the percentage of homes in the subdivision sold over the 6 month period.

[pic]

What percentage of the homes were sold in the 4th month?

|[pic|A. |50% of homes |

|] | | |

|[pic|B. |30% of homes |

|] | | |

|[pic|C. |75% of homes |

|] | | |

|[pic|D. |20% of homes |

|] | | |

|[pic|E. |80% of homes |

|] | | |

[pic]

Stemplots

2. The stemplot below shows the number of points scored in each game by the Tigers and the Bears in one football season.

Points Scored

|Tigers | | | |Bears |

| | | | | |

|7 7 3 0 |[|0 |[|0 0 3 3 7 |

| |p| |p| |

| |i| |i| |

| |c| |c| |

| |]| |]| |

|7 7 4 4 0 | |1 | |0 0 4 7 |

|7 3 1 0 | |2 | |0 1 1 4 4 8 |

|2 2 1 | |3 | |5 |

Which of the following is true regarding the data sets above?

I. The mean of the Tigers' scores is greater than the mean of the Bears' scores.

II. The median of the Tigers' scores is less than the median of the Bears' scores.

III. The range of the Tigers' scores is less than the range of the Bears' scores.

|[pic|A. |I and III |

|] | | |

|[pic|B. |I and II |

|] | | |

|[pic|C. |II and III |

|] | | |

|[pic|D. |I only |

|] | | |

|[pic|E. |All statements are true. |

|] | | |

[pic]

Histograms

3. The histograms below show the finishing times for a swim team's first competition and last competition of a season.

[pic]

Which of the following are true regarding the data sets above?

I. The first competition's distribution is skewed left, and the last competition's distribution is skewed left.

II. The first competition's distribution is skewed right, and the last competition's distribution is skewed right.

III. The first competition's distribution is skewed left, and the last competition's distribution is skewed right.

IV. The first competition's distribution is skewed right, and the last competition's distribution is skewed left.

V. The data set for first competition contains an outlier.

|[pic|A. |I and V |

|] | | |

|[pic|B. |V only |

|] | | |

|[pic|C. |II only |

|] | | |

|[pic|D. |I only |

|] | | |

|[pic|E. |II and V |

|] | | |

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Data Collection

4. Tom is planting a garden. He plants three identical tomato plants in the same soil. Each plant receives the same amount of sunlight and water. The first tomato plant receives store-bought fertilizer. The second tomato plant receives homemade fertilizer. The third tomato plant does not receive any fertilizer.

Which of the following methods is being used to investigate the effect of different fertilizers on the rate of growth of the tomato plants?

|[pic|A. |observational study |

|] | | |

|[pic|B. |separation study |

|] | | |

|[pic|C. |survey |

|] | | |

|[pic|D. |controlled experiment |

|] | | |

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Categorical Data

5. Sam opens a new sandwich shop. The shop has two speciality sandwiches: Sam's Turkey and Sam's Ham. The monthly sales over a four month period are shown in the bar charts below.

[pic]

What can be concluded about the popularity of each sandwich from the information above?

|[pic|A. |Sam's Turkey sandwich grew in popularity, and Sam's Ham sandwich declined in popularity. |

|] | | |

|[pic|B. |The number of Sam's Ham sandwiches sold exceeds the number of Sam's Turkey sandwiches sold over the four month period. |

|] | | |

|[pic|C. |Sam's Ham sandwich and Sam's Turkey sandwich maintained their popularity over the four month period. |

|] | | |

|[pic|D. |There is not enough information to make conclusions regarding the popularity of the sandwiches. |

|] | | |

|[pic|E. |Sam's Ham sandwich grew in popularity, and Sam's Turkey sandwich declined in popularity. |

|] | | |

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Probability

6. Mark has 13 shirts in his closet. He has 6 long-sleeve shirts that are solid, and he has 10 shirts that are solid. What is the probability that a shirt has long sleeves given that it is solid?

|[pic|A. |[pic] |

|] | | |

|[pic|B. |[pic] |

|] | | |

|[pic|C. |[pic] |

|] | | |

|[pic|D. |[pic] |

|] | | |

|[pic|E. |[pic] |

|] | | |

[pic]

Central Tendency and Spread

7. What is the mean of the number set below?

39.6 , 55.9 , 63.5 , 35.1 , 49.2 , 30.4 , 61 , 58.7

|[pic|A. |39.34 |

|] | | |

|[pic|B. |49.175 |

|] | | |

|[pic|C. |52.55 |

|] | | |

|[pic|D. |56.2 |

|] | | |

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Stemplots

8. The stemplot below shows the ages of the employees at Jan's Restaurant.

Employee Age

|1 |[|6 6 7 8 9 |

| |p| |

| |i| |

| |c| |

| |]| |

|2 | |0 0 0 1 2 3 9 |

|3 | |5 7 8 |

|4 | | |

|5 | | |

|6 | |5 |

Which of the following is true regarding the data set above?

I. The data is skewed left.

II. The data is skewed right.

III. The data is symmetric.

IV. The data possesses a gap.

|[pic|A. |I and IV |

|] | | |

|[pic|B. |II and IV |

|] | | |

|[pic|C. |III only |

|] | | |

|[pic|D. |II only |

|] | | |

|[pic|E. |I only |

|] | | |

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Independent and Dependent Variables

9. A contractor currently has 11 construction workers working on a building. When the building is finished, it will have 20 stories. If he increases the number of workers to 44, the building will be done four times as quickly. Which statement best describes the time it takes to complete the building?

|[pic|A. |The time it takes to complete the building is both an independent and a dependent variable. |

|] | | |

|[pic|B. |The time it takes to complete the building is both a dependent and a constant variable. |

|] | | |

|[pic|C. |The time it takes to complete the building is the constant variable. |

|] | | |

|[pic|D. |The time it takes to complete the building is the dependent variable. |

|] | | |

|[pic|E. |The time it takes to complete the building is the independent variable. |

|] | | |

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Dotplots

10. The dotplot below shows the number of scholarship applications submitted by a group of seniors.

Scholarship Applications

|0 |[|* |

| |p| |

| |i| |

| |c| |

| |]| |

|1 | |*  *  *  *  *  * |

|2 | |*  *  *  *  *  *  * |

|3 | |*  *  *  * |

|4 | | |

|5 | | |

|6 | |*  *  *  *  * |

|7 | |*  *  * |

Which of the following is true regarding the data set above?

I. The mean of the data is 3.5.

II. The range of the data is 6.

III. The data is symmetric.

IV. The data possesses a gap.

|[pic|A. |II and IV |

|] | | |

|[pic|B. |I only |

|] | | |

|[pic|C. |III only |

|] | | |

|[pic|D. |IV only |

|] | | |

|[pic|E. |I and IV |

|] | | |

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Dotplots

11. The dotplot below shows the number of goals scored per game by the Raiders in a single season.

Number of Goals Scored Per Game

|* |

|* |

|0 |1 |2 |

|[pic|B. |2.6 |

|] | | |

|[pic|C. |2.8 |

|] | | |

|[pic|D. |1.8 |

|] | | |

|[pic|E. |2 |

|] | | |

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The Normal Distribution

12. The sitting height (from the bottom of the seat to the top of the person's head) of male drivers is normally distributed with a mean of 36 inches and a standard deviation of 1.4 inches as shown below.

[pic]

If a car company wants to design a vehicle so that 99.9% of men fit in the driver's seat, how high from the bottom of the seat must they make the roof?

|[pic|A. |31.8 in. |

|] | | |

|[pic|B. |40.2 in. |

|] | | |

|[pic|C. |37.4 in. |

|] | | |

|[pic|D. |38.8 in. |

|] | | |

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Independent and Dependent Variables

13. On average, the more years of education a person has, the higher the salary he or she will have. What is the dependent variable in this statement?

|[pic|A. |salary |

|] | | |

|[pic|B. |number of years of education |

|] | | |

|[pic|C. |number of years spent working at the same company |

|] | | |

|[pic|D. |position in a company |

|] | | |

|[pic|E. |The patient's fever is the independent variable. |

|] | | |

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Scatterplots

14. An ice cream company has discovered that the number of ice cream cones sold in one hour is related to the temperature outside. A collection of data from two different stores on the outside temperature and number of cones sold produced the dotplot below.

[pic]

Without finding the equations, compare the regression models for Store A's data and Store B's data.

|[pic|A. |The models will have the same slope but different intercepts because of an influential point. |

|] | | |

|[pic|B. |The models will have a different slopes and different intercepts because of an influential point. Store A's slope will be greater |

|] | |than Store B's slope. |

|[pic|C. |The models will be the same because the data points are the same. |

|] | | |

|[pic|D. |The models will have a different slopes and different intercepts because of an influential point. Store A's slope will be less than|

|] | |Store B's slope. |

|[pic|E. |The models will have the same intercepts but different slopes because of an influential point. Store A's slope will be less than |

|] | |Store B's slope. |

[pic]

Central Tendency and Spread

15. Ron is a waiter at a restaurant. He worked five shifts this week and made $69, $77, $71, $90, and $73 in tips during each shift respectively. What is the mean for his tips during a shift?

|[pic|A. |$76 |

|] | | |

|[pic|B. |$71 |

|] | | |

|[pic|C. |$90 |

|] | | |

|[pic|D. |$77 |

|] | | |

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Box Plots

16. Which of the following box plots is skewed left?

|[pic] |[pic] |

|W. |X. |

|[pic] |[pic] |

|Y. |Z. |

|[pic|A. |W |

|] | | |

|[pic|B. |There are no box plots shown that are skewed left. |

|] | | |

|[pic|C. |Z |

|] | | |

|[pic|D. |Y |

|] | | |

|[pic|E. |X |

|] | | |

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Stemplots

17. The stemplot below shows the ages of a garden club's members.

Member Age

|2 |[|9 |

| |p| |

| |i| |

| |c| |

| |]| |

|3 | |0 3 6 |

|4 | |1 5 |

|5 | |2 2 3 9 |

|6 | |0 0 0 0 |

|7 | | |

|8 | |2 |

Find the mean of the ages.

|[pic|A. |54.8 |

|] | | |

|[pic|B. |53 |

|] | | |

|[pic|C. |52 |

|] | | |

|[pic|D. |50.1 |

|] | | |

|[pic|E. |47 |

|] | | |

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Random Variables and Probability Distributions

18. Which of the following is a continuous random variable?

|[pic|A. |The number of windows in the White House. |

|] | | |

|[pic|B. |The speed of a car. |

|] | | |

|[pic|C. |The number of pages in a book. |

|] | | |

|[pic|D. |The number of points scored in a basketball game. |

|] | | |

|[pic|E. |The number of acorns on an oak tree. |

|] | | |

[pic]

Cumulative Frequency Plots

19. An organization is selling cookies to pay for a camping trip. Each member of the organization is assigned boxes of cookies to sell over a 4 week period. The frequency table below show the number of boxes sold by week.

|Week |0 - 1 |1 - 2 |2 - 3 |3 - 4 |

|Frequency |200 |500 |300 |500 |

Choose the ogive curve that represents the frequency table above.

|[pic] |[pic] |

|W. |X. |

|[pic] |[pic] |

|Y. |Z. |

|[pic|A. |Z |

|] | | |

|[pic|B. |X |

|] | | |

|[pic|C. |W |

|] | | |

|[pic|D. |Y |

|] | | |

|[pic|E. |The correct graph is not shown. |

|] | | |

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Surveys

20. A researcher wants to determine the percentage of high school students that drive and text message in a particular state.

Which of the following methods would assure random selection of a sample population?

|I) | |The researcher should randomly select one high school in the state and survey each student enrolled. |

| | | |

|II) | |The researcher should survey all high school students in the state. |

| | | |

|III) | |The researcher should randomly select one high school in the state and survey randomly selected students within the school. |

| | | |

|IV) | |The researcher should randomly select a city in the state and survey all high school students that reside within the city. |

| | | |

|V) | |The researcher should randomly select students from all high school students that reside within the state. |

|[pic|A. |V |

|] | | |

|[pic|B. |IV |

|] | | |

|[pic|C. |III |

|] | | |

|[pic|D. |II |

|] | | |

|[pic|E. |I|

|] | | |

[pic]

Histograms

21. The histogram below shows the number of sales calls Adam conducted in a business day.

[pic]

Which of the following is true?

|[pic|A. |The histogram is bimodal. |

|] | | |

|[pic|B. |The histogram is symmetric. |

|] | | |

|[pic|C. |The histogram has an outlier. |

|] | | |

|[pic|D. |The histogram is contains a gap. |

|] | | |

|[pic|E. |The histogram is multimodal. |

|] | | |

[pic]

The Normal Distribution

22. The amount 5th grade students grow during the school year is normally distributed with a mean of 4 inches and a standard deviation of 1 inch. The amount 6th grade students grow during the school year is normally distributed as well. They have a mean of 4 inches and a standard deviation of 1 inch. Both distributions are shown below.

|[pic] |[pic] |

What percentage of 5th and 6th graders grow between 2 inches and 4 inches?

|[pic|A. |49.7% |

|] | | |

|[pic|B. |It is not possible to answer the question because it is not appropriate to use a normal distribution when there are two separate |

|] | |peaks. |

|[pic|C. |54.6% |

|] | | |

|[pic|D. |47.5% |

|] | | |

[pic]

The Normal Distribution

23. Intelligence quotient test scores are distributed normally and have a mean of 100 with a standard deviation of 15. Calculate the z-score of a 110 IQ and round to the nearest hundredth.

|[pic|A. |[pic]0.67 |

|] | | |

|[pic|B. |[pic]0.33 |

|] | | |

|[pic|C. |[pic]1.67 |

|] | | |

|[pic|D. |= 1 |

|] | | |

[pic]

Stemplots

24. The stemplot below shows the ages of a garden club's members.

Member Age

|2 |[|9 |

| |p| |

| |i| |

| |c| |

| |]| |

|3 | |0 3 6 |

|4 | |1 5 |

|5 | |2 2 3 9 |

|6 | |0 0 0 0 |

|7 | | |

|8 | |2 |

Find the mode of the ages.

|[pic|A. |52 |

|] | | |

|[pic|B. |53 |

|] | | |

|[pic|C. |50.1 |

|] | | |

|[pic|D. |60 |

|] | | |

|[pic|E. |82 |

|] | | |

[pic]

Experiments

25. A company is conducting an experiment to test a new nutritional supplement. The company randomly selects 2000 subjects. Half of the subjects are males, and the other half of the subjects are females. The ages of the subjects range from 18 to 69.

The company creates pairs of males and pairs of females. One member from each individual pair receives the nutritional supplement, while the other member receives a placebo.

Which of the following experimental designs describes the experiment above?

|I) | |Completely Randomized Design |

|II) | |Randomized Block Design |

|III) | |Matched Pairs Design |

|IV) | |Randomized Pairs Design |

|[pic|A. |IV |

|] | | |

|[pic|B. |I|

|] | | |

|[pic|C. |II |

|] | | |

|[pic|D. |III |

|] | | |

|[pic|E. |The design type is not listed. |

|] | | |

[pic]

Surveys

26. Lydia wants to conduct a survey regarding her high school's uniform policy. Which technique would assure that Lydia's survey is well-designed and well-conducted?

|[pic|A. |Lydia should choose her closest friends to represent the entire student population. She should then randomly select a group of her |

|] | |closest friends and administer the survey to her randomly selected friends. |

|[pic|B. |Lydia should randomly select a sample of students from the entire student population. She should then administer the survey to all |

|] | |of the randomly selected students. |

|[pic|C. |Lydia should randomly select one class to represent the entire student population. She should then administer the survey to all |

|] | |students in the randomly selected class. |

|[pic|D. |Lydia should select one grade to represent the entire student population. She should then randomly select students in the selected |

|] | |grade and administer the survey to the randomly selected students. |

|[pic|E. |Lydia should randomly select one grade to represent the entire student population. She should then administer the survey to all |

|] | |students in the randomly selected grade. |

[pic]

Data Collection

27. Janis enjoys making bread and wants to investigate the rate of mold growth on bread. She makes bread dough and then the dough is divided into two even loaves. The loaves are then baked and cooled equivalently. One loaf is then left on the counter, while the other loaf is placed in a air tight container. Which of the following methods is being used to investigate the rate of mold growth on the bread?

|[pic|A. |separation study |

|] | | |

|[pic|B. |experimental study |

|] | | |

|[pic|C. |observational study |

|] | | |

|[pic|D. |controlled experiment |

|] | | |

[pic]

Box Plots

28. Which of the following box plots is symmetric?

|[pic] |[pic] |

|W. |X. |

|[pic] |[pic] |

|Y. |Z. |

|[pic|A. |Z |

|] | | |

|[pic|B. |X |

|] | | |

|[pic|C. |W |

|] | | |

|[pic|D. |Y |

|] | | |

|[pic|E. |There are no box plots shown that are symmetric. |

|] | | |

[pic]

Dotplots

29. The dotplot below shows the number of school sports and activities participated in by a group of male students and a group of female students at Franklin High School.

Sport and Activity Participation

|Male Students | | | |Female Students | |

| | | | | | |

|*  *  *  *  * |[|0 |[|*  * | |

| |p| |p| | |

| |i| |i| | |

| |c| |c| | |

| |]| |]| | |

|*  *  *  * | |1 | | | |

|*  * | |2 | | | |

|*  * | |3 | |*  *  *  *  * | |

|*  * | |4 | |*  *  *  *  *  *  *  * | |

Which of the following is true regarding the data set above?

I. The data set for male students possesses a gap.

II. The data set for female students possesses a gap.

III. The mean of the male student data is less than the mean of the female student data.

IV. The mean of the female student data is less than the mean

of the male student data.

|[pic|A. |II and III |

|] | | |

|[pic|B. |I and IV |

|] | | |

|[pic|C. |I and III |

|] | | |

|[pic|D. |II and IV |

|] | | |

|[pic|E. |III only |

|] | | |

[pic]

Random Variables and Probability Distributions

30. A research agency conducted a survey of 1,900 families, asking them how many children they had. The following table lists the frequency distribution of the data collected.

|Number of |0 |1 |2 |3 |4 |

|Children | | | | | |

|Number of |38 |437 |1,045 |228 |152 |

|Families | | | | | |

What is the probability that a family chosen from this group at random will have 1 child?

|[pic|A. |0.23 |

|] | | |

|[pic|B. |0.25 |

|] | | |

|[pic|C. |0.02 |

|] | | |

|[pic|D. |0.98 |

|] | | |

|[pic|E. |0.28 |

|] | | |

[pic]

Categorical Data

31. The two-way frequency table below shows the extracurricular activities of juniors and seniors at Franklin High School.

Extracurricular Activities

| |Band |Athletics |Drama Club |Total |

|Male |90 |180 |45 |315 |

|Female |95 |135 |45 |275 |

|Total |185 |315 |90 |590 |

Which of the following can be concluded from the marginal frequencies of the table above?

I. The most popular extracurricular activity is athletics.

II. There is more female involvement in extracurricular activities than male involvement.

III. There is more male involvement in extracurricular activities than female involvement.

IV. Drama club is the least popular extracurricular activity.

|[pic|A. |II and IV only |

|] | | |

|[pic|B. |I, III, and IV |

|] | | |

|[pic|C. |III and IV only |

|] | | |

|[pic|D. |I, II, and IV |

|] | | |

|[pic|E. |I and IV only |

|] | | |

[pic]

Dotplots

32. The dotplot below shows the number of books read over summer break by each student in Mr. Smith's English class.

Number of Books Read

|0 |[|*  * |

| |p| |

| |i| |

| |c| |

| |]| |

|1 | |*  *  *  * |

|2 | |*  *  *  *  *  *  *  *  *  * |

|3 | |*  *  *  * |

|4 | |*  * |

Which of the following is true regarding the data set above?

I. The data is skewed left.

II. The data is skewed right.

III. The data is symmetric.

IV. The median of the data is 2.

|[pic|A. |I and IV |

|] | | |

|[pic|B. |IV only |

|] | | |

|[pic|C. |III only |

|] | | |

|[pic|D. |III and IV |

|] | | |

|[pic|E. |II and IV |

|] | | |

[pic]

Central Tendency and Spread

33. The frequency table shows the average number of hours Talia spends each week practicing singing. What is the mode of the average hours?

WEEKLY AVERAGE HOURS OF

SINGING PRACTICE

|Average Hours |Frequency |

|4 |2 |

|5 |5 |

|6 |4 |

|7 |7 |

|8 |2 |

|[pic|A. |7 hours |

|] | | |

|[pic|B. |6 hours |

|] | | |

|[pic|C. |4 hours |

|] | | |

|[pic|D. |5 hours |

|] | | |

[pic]

Experiments

34. A drug company is testing a new influenza medicine. The company selects 100 adults, with the same strain of influenza, to randomly form two groups: a control group and a treatment group. The participants are unaware of their placements. The control group receives a placebo, while the treatment group receives the influenza medicine. After 3 days, 25% of the control group showed signs of improvement, even though they were only receiving a placebo.

Which of the following terms best explains the improvement in the control group?

|[pic|A. |placebo effect |

|] | | |

|[pic|B. |bias |

|] | | |

|[pic|C. |randomization |

|] | | |

|[pic|D. |blinding |

|] | | |

|[pic|E. |blocking |

|] | | |

[pic]

Surveys

35. A restaurant is conducting a survey regarding the quality of its food. The restaurant owner prints a website on the bottom of all food receipts for an online survey.

State the type of bias that the survey presents.

|[pic|A. |nonresponse bias |

|] | | |

|[pic|B. |the survey is not subject to bias |

|] | | |

|[pic|C. |voluntary response bias |

|] | | |

|[pic|D. |undercoverage |

|] | | |

|[pic|E. |response bias |

|] | | |

[pic]

Probability

36. Ryan's mp3 player has 34 songs on it. There are 12 country songs, 10 rock songs, and 12 jazz songs. If Ryan randomly selects 2 songs, without replacement, what is the probability that one song will be country and one song will be rock?

|[pic|A. |[pic] |

|] | | |

|[pic|B. |[pic] |

|] | | |

|[pic|C. |[pic] |

|] | | |

|[pic|D. |[pic] |

|] | | |

|[pic|E. |[pic] |

|] | | |

[pic]

Independent and Dependent Variables

37. A contractor currently has 16 construction workers working on a building. When the building is finished, it will have 20 stories. If he increases the number of workers to 32, the building will be done twice as quickly. Which statement best describes the height of the building in this situation?

|[pic|A. |The height of the building is the independent variable. |

|] | | |

|[pic|B. |The height of the building is both an independent and a dependent variable. |

|] | | |

|[pic|C. |The height of the building is the dependent variable. |

|] | | |

|[pic|D. |The height of the building is neither an independent nor a dependent variable. |

|] | | |

|[pic|E. |The height of the building is both an independent and a constant variable. |

|] | | |

[pic]

Data Collection

38. Which of the following would be the best method for investigating the wind speeds of hurricanes?

|[pic|A. |questionnaire study |

|] | | |

|[pic|B. |observational study |

|] | | |

|[pic|C. |experimental study |

|] | | |

|[pic|D. |survey |

|] | | |

[pic]

Categorical Data

39. A group of students were asked to choose their favorite sport. The results are shown in the two-way frequency table below.

Favorite Sport

| |Football |Baseball |Basketball |Soccer |Total |

|Male |49 |42 |28 |35 |154 |

|Female |14 |21 |28 |49 |112 |

|Total |63 |63 |56 |84 |266 |

What percentage of females chose soccer as their favorite sport?

|[pic|A. |13.16% |

|] | | |

|[pic|B. |18.42% |

|] | | |

|[pic|C. |22.73% |

|] | | |

|[pic|D. |43.75% |

|] | | |

|[pic|E. |31.58% |

|] | | |

[pic]

Cumulative Frequency Plots

40.

[pic]

Jim and Bill each have a 6 month sales goal. The cumulative percentage plots above display the monthly progress toward each employee's goal. Which of the following statements are true?

I. Jim and Bill both met their 6 month sales goal.

II. Jim met the median of his sales goal in the 3rd month, while Bill met the median of his sales goal in the 2nd month.

III. The greatest percentage of sales for Jim was in the 5th month.

IV. The greatest percentage of sales for both Jim and Bill was in the 6th month.

|[pic|A. |I and II |

|] | | |

|[pic|B. |II only |

|] | | |

|[pic|C. |I only |

|] | | |

|[pic|D. |IV only |

|] | | |

|[pic|E. |I and III |

|] | | |

[pic]

Random Variables and Probability Distributions

41. A glass maker recycles 37% of the vases they make because of imperfections and their high standards. If 8 vases are randomly chosen and inspected, what is the probability that 3 or 4 of them will not pass inspection and be recycled?

|[pic|A. |0.20667 |

|] | | |

|[pic|B. |1.7829 |

|] | | |

|[pic|C. |0.27146 |

|] | | |

|[pic|D. |0.47813 |

|] | | |

|[pic|E. |0.3003 |

|] | | |

[pic]

Scatterplots

42. The weekly cost of groceries for a household is related to the number of people that reside in the household. A collection of data on household size and the weekly cost of groceries of 10 households produced the scatterplot below.

[pic]

Using the least squares method, write a linear regression equation that models the data above.

|[pic|A. |[pic] |

|] | | |

|[pic|B. |[pic] |

|] | | |

|[pic|C. |[pic] |

|] | | |

|[pic|D. |[pic] |

|] | | |

|[pic|E. |[pic] |

|] | | |

[pic]

Box Plots

43. A cell phone company conducted a survey regarding cell phone usage of high school students. The company was specifically interested in the difference between male cell phone usage and female cell phone usage. The cell phone company produced the box plots below to show the number of cellular minutes that male and female students used in one month.

Cell Phone Usage

[pic]

Which of the following statements are true regarding the box plots above?

I. About 50 percent of female students use 1000 to 1200 cellular minutes a month.

II. About 25 percent of male students use 300 to 400 cellular minutes a month.

III. The median of female cell phone minute usage is greater than the median of male cell phone usage.

IV. The interquartile range of female cell phone minute usage is greater than the interquartile range of male cell phone minute usage.

|[pic|A. |II and III |

|] | | |

|[pic|B. |II and IV |

|] | | |

|[pic|C. |I and IV |

|] | | |

|[pic|D. |III and IV |

|] | | |

|[pic|E. |I and III |

|] | | |

[pic]

Box Plots

44. The box plot below represents the finishing times, in seconds, of swimmers in a competition. What percentage of swimmers completed the competition in 30 seconds or less?

Swimming Competition Finshing Times

[pic]

Time (seconds)

|[pic|A. |50 percent |

|] | | |

|[pic|B. |25 percent |

|] | | |

|[pic|C. |30 percent |

|] | | |

|[pic|D. |5 percent |

|] | | |

|[pic|E. |75 percent |

|] | | |

[pic]

Probability

45. Sam's closet contains blue and green shirts. He has eight blue shirts, and seven green shirts. Five of the blue shirts have stripes, and four of the green shirts have stripes. What is the probability that Sam randomly chooses a shirt that is blue or has stripes?

|[pic|A. |[pic] |

|] | | |

|[pic|B. |[pic] |

|] | | |

|[pic|C. |[pic] |

|] | | |

|[pic|D. |[pic] |

|] | | |

|[pic|E. |[pic] |

|] | | |

[pic]

Histograms

46. Timothy is conducting a study regarding adults and exercise. He surveyed a sample of adults regarding their exercise habits, and he recorded his findings in the histogram below.

[pic]

Which of the following are true?

I. This histogram is unimodal.

II. The histogram is bimodal.

III. The histogram is symmetric.

IV. The histogram is skewed left.

V. The histogram is skewed right.

|[pic|A. |I only |

|] | | |

|[pic|B. |II and III |

|] | | |

|[pic|C. |II and V |

|] | | |

|[pic|D. |II and IV |

|] | | |

|[pic|E. |I and III |

|] | | |

[pic]

Scatterplots

47. Choose the scatterplot with positive correlation.

|[pic] |[pic] |

|W. |X. |

|[pic] |[pic] |

|Y. |Z. |

|[pic|A. |The correct graph is not shown. |

|] | | |

|[pic|B. |X |

|] | | |

|[pic|C. |Y |

|] | | |

|[pic|D. |W |

|] | | |

|[pic|E. |Z |

|] | | |

[pic]

Central Tendency and Spread

48. Retread is a used car lot where they line up the cars according to price. Today the front row contains the following prices: $10,100, $6,400, $8,400, $8,700, $9,100, $10,100, and $9,100. What is the median price in the front row?

|[pic|A. |$10,100 |

|] | | |

|[pic|B. |$8,900 |

|] | | |

|[pic|C. |$9,100 |

|] | | |

|[pic|D. |$8,843 |

|] | | |

[pic]

Experiments

49. A bontanist is conducting an experiment to test a new fertilizer that has been developed for roses. The bontanist has selected 800 experimental units. Half of the experimental units are red roses, and the other half of the experimental units are white roses. All units are of equal maturity levels.

The bontanist creates pairs of red roses and pairs of white roses. One plant in each individual pair will receive fertilizer. The other plant in the pair will not receive any fertilizer.

Which of the following experimental designs describes the experiment above?

|I) | |Completely Randomized Design |

|II) | |Randomized Block Design |

|III) | |Matched Pairs Design |

|IV) | |Randomized Pairs Design |

|[pic|A. |I|

|] | | |

|[pic|B. |III |

|] | | |

|[pic|C. |II |

|] | | |

|[pic|D. |The design type is not listed. |

|] | | |

|[pic|E. |IV |

|] | | |

[pic]

Histograms

50. The histogram below shows a particular high school's enrollment.

[pic]

Which of the following are true?

I. The histogram is unimodal.

II. The histogram is bimodal.

III. The histogram is multimodal.

IV. The histogram has a uniform distribution.

V. The histogram is symmetric.

|[pic|A. |I and IV |

|] | | |

|[pic|B. |V |

|] | | |

|[pic|C. |III |

|] | | |

|[pic|D. |IV and V |

|] | | |

|[pic|E. |II and IV |

|] | | |

[pic]

Answers

1. B

2. A

3. A

4. D

5. A

6. D

7. B

8. B

9. D

10. D

11. B

12. B

13. A

14. D

15. A

16. C

17. D

18. B

19. C

20. A

21. D

22. D

23. A

24. D

25. D

26. B

27. D

28. C

29. A

30. A

31. B

32. D

33. A

34. A

35. D

36. A

37. D

38. B

39. D

40. A

41. D

42. A

43. A

44. B

45. B

46. B

47. E

48. C

49. B

50. D

1. 30% of homes

2. I and III

3. I and V

4. controlled experiment

5. Sam's Turkey sandwich grew in popularity, and Sam's Ham sandwich declined in popularity.

6. [pic]

7. 49.175

8. II and IV

9. The time it takes to complete the building is the dependent variable.

10. IV only

11. 2.6

12. 40.2 in.

13. salary

14. The models will have a different slopes and different intercepts because of an influential point. Store A's slope will be less than Store B's slope.

15. $76

16. Z

17. 50.1

18. The speed of a car.

19. W

20. V

21. The histogram is contains a gap.

22. 47.5%

23. [pic]0.67

24. 60

25. III

26. Lydia should randomly select a sample of students from the entire student population. She should then administer the survey to all of the randomly selected students.

27. controlled experiment

28. W

29. II and III

30. 0.23

31. I, III, and IV

32. III and IV

33. 7 hours

34. placebo effect

35. undercoverage

36. [pic]

37. The height of the building is neither an independent nor a dependent variable.

38. observational study

39. 43.75%

40. I and II

41. 0.47813

42. [pic]

43. II and III

44. 25 percent

45. [pic]

46. II and III

47. Z

48. $9,100

49. III

50. IV and V

Explanations

1. The category of the 4th month represents the total percentage of homes sold in the first 4 months. The question only asks for the percentage of homes sold in the 4th month. To find this percentage, subtract.

|Percentage of Homes Sold in Month 4 |= |Cumulative Percentage in Month 4 - Cumulative Percentage in Month 3 |

| |= |80% - 50% |

| |= |30% |

In the 4th month, 30% of the homes were sold.

2. Mean

The mean of the data set can be found by adding all of the entries together and dividing by the total number of entries.

Find the mean of the Tigers' scores.

|(0 + 3 + 7 + 7 + 10 + 14 + 14 + 17 + 17 + 20 + 21 + 23 + 27 + 31 + 32 + 32) ÷ 16 |= |275 ÷ 16 |

| |[pic] |17.188 |

Find the mean of the Bears' scores.

|(0 + 0 + 3 + 3 + 7 + 10 + 10 + 14 + 17 + 20 + 21 + 21 + 24 + 24 + 28 + 35) ÷ 16 |= |237 ÷ 16 |

| |[pic] |14.813 |

The mean of the Tigers' scores is greater than the mean of the Bears' scores.

Median

The median of an ordered data set is the middle value.

Find the median of the Tigers' scores.

|17 + 17 |= | 17 |

| | | |

|[pic] | | |

| | | |

|2 | | |

| | | |

Find the median of the Bears' scores.

|14 + 17 |= | 15.5 |

| | | |

|[pic] | | |

| | | |

|2 | | |

| | | |

The median of the Tigers' scores is greater than the median of the Bears' scores.

Range

The range of the data set is the difference between the largest and smallest values.

Find the range of the Tigers' scores.

|Range of Tigers' Scores |= |32 - 0 |

| |= |32 |

Find the range of the Bears' scores.

|Range of Bears' Scores |= |35 - 0 |

| |= |35 |

The range of the Tigers' scores is less than the range of the Bears' scores.

Given the information above, II and IV are both true statements.

3. Skewness

Skewness occurs when the entries of the data set are either distributed more to the left or more to the right.

Most of the entries for the first competition lie to the right; therefore, the data set is said to be skewed left.

Most of the entries for the second competition lie to the right; therefore, the data set is said to be skewed left.

The first competition's distribution is skewed left, and the last competition's distribution is skewed left.

Outlier

The outlier of a data set is the entry that varies greatly from the other entries in the data set. An outlier typically lies at least 1.5 interquartile ranges below the first quartile or 1.5 interquartile ranges above the third quartile.

In the first competition's data set, there is an outlier for the time interval of 30 to 60 seconds.

In the last competition's data set, there is not a value that lies at least 1.5 interquartile ranges below the first quartile or 1.5 interquartile ranges above the third quartile; therefore, the data set does not have an outlier.

The first competition's data set has an outlier.

Given the information above, both I and V are true statements.

4. In a controlled experiment, the researcher separates the sample population into groups with one group designated as the control group.

All groups are manipulated in some way, except for the control group which remains the same.

5. A bar chart is a graph composed of bins, or equal-width columns. Each bin represents a categorical variable, and the height of each bin represents the size of the category.

The heights of the bins in the bar chart displaying the monthly sales of Sam's Turkey sandwiches are growing each month; therefore, it can be concluded that the sandwich is growing in popularity.

The heights of the bins in the bar chart displaying the monthly sales of Sam's Ham sandwiches are declining each month; therefore, it can be concluded that the sandwich is declining in popularity.

Sam's Turkey sandwich grew in popularity, and Sam's Ham sandwich declined in popularity.

6. Given that A and B are compound events, use the following conditional probability formula to find the probability that event B will occur given that the event A has already occurred.

[pic]

Define the events.

[pic]

The question asks for the probability that a shirt has long sleeves given that the shirt is solid; therefore, the formula for conditional probability must be applied.

Rewrite the formula for conditional probability for the given events, S and L.

[pic]

Find P(S). Mark has 13 shirts, and 10 shirts are solid.

[pic]

Find P(S [pic]L). Mark has 13 shirts, and 6 of the shirts are solid and have long sleeves.

[pic]

Substitute P(S) and P(S [pic]L) into the formula for conditional probability and simplify to obtain the final answer.

[pic]

7. To find the mean, add the numbers together and divide by 8.

39.6 + 55.9 + 63.5 + 35.1 + 49.2 + 30.4 + 61 + 58.7 = 393.4

393.4 ÷ 8 = 49.175

The mean of this set of numbers is 49.175.

8. Skewness occurs when the entries of the data set are either distributed more to the left or more to the right. In this case, most of the entries, lie to the left; therefore, the data set is said to be skewed right. Given that the data set is skewed right, it can not be symmetric.

Gaps are areas of distribution with no observations. In this case, there is a gap in the ages of 40 and 50. The data set is, therefore, said to contain a gap.

Given the above information, both II and IV are true statements.

9. An independent variable is a variable whose value determines the value of other variables, and it is changed in an experiment to see its effect on other variables.

A variable that changes because of a change in the independent variable is a dependent variable.

In this situation, changing the number of construction workers changes the amount of time it will take to complete the building.

Therefore, the time it takes to complete the building is the dependent variable in this situation.

10. The mean of the data set can be found by adding all of the entries together and dividing by the total number of entries. There are 26 total entries in this data set. Add all numbers together, and divide by 26. The mean of the scholarship applications is 83 ÷ 26 = 3.2.

The range of the data set is the difference between the largest and smallest values. Find the smallest number of scholarship applications, and subtract it from the largest number of scholarship applications. The range of the scholarship applications is 7 - 0 = 7.

Symmetry occurs when the entries of the data set are equally distributed on both sides of the median. In this case, the median of the data set is 2. It is seen that the other entries are not equally distributed on the left and on the right of the median; therefore, the data set is not symmetric.

Gaps are areas of distribution with no observations. In this case, there is a gap in the scholarship application numbers of 4 and 5. The data set is, therefore, said to contain a gap.

Given the above information, only IV is a true statement.

11. The mean of the data set can be found by adding all of the entries together and dividing by the total number of entries. Remember that each dot represents a single entry. There are 25 total entries in this data set. Add all numbers together, and divide by 25.

65 ÷ 25 = 2.6

12. When given a normal distribution graph, the peak represents the mean of the data and the following properties apply.

• About 68% of the data lies within 1 standard deviation of the mean.

• About 95% of the data lies within 2 standard deviations of the mean.

• About 99.8% of the data lies within 3 standard deviations of the mean.

The following graph illustrates these properties.

[pic]

From the answer choices, calculate the percentage of men who would fit if the height of the roof was 36 in.

34% + 13.5% + 2.4% + 0.1% = 50%

Next, calculate the percentage of men who would fit if the height of the roof was 38.8 in.

13.5% + 34% + 34% + 13.5% + 2.4% + 0.1% = 97.5

Third, calculate the percentage of men who would fit if the height of the roof was 37.4 in.

34% + 34% + 13.5% + 2.4% + 0.1% = 84%

Finally, calculate the percentage of men who would fit if the height of the roof was 40.2 in.

2.4% + 13.5% + 34% + 34% + 13.5% + 2.4% + 0.1% = 99.9%

Therefore, in order for 99.9% of men to fit in the driver's seat, they must make the roof 40.2 in. from the bottom of the seat.

13. An independent variable is a variable whose value determines the value of other variables, and it is changed in an experiment to see its effect on other variables.

A variable that changes because of a change in the independent variable is a dependent variable.

According to the statement in the question, a person's salary changes based on a change to the number of years of education he or she has.

Therefore, the dependent variable in the statement is salary.

14. An influential point is a single point that strongly influences the slope and the intercept of a regression model. If an influential point is removed from the data, the data will yield a very different model.

The data points for Store A and Store B are the same except for one point. Store B has an addition data point at 100o. The data point at 100o is called an influential point; therefore, it will cause the model for Store B to differ than the model for Store A. In this case, the influential point causes the model of Store B to have a greater slope than the model of Store A.

The models will have a different slopes and different intercepts because of th influential point. Store A's slope will be less than Store B's slope.

15. To find the mean, first find the sum of the values in the set. Then divide the sum by the number of values in the set.

Sum = $69 + $77 + $71 + $90 + $73 = $380

Mean = $380 ÷ 5 = $76

16. Skewness occurs when the entries of the data set are either distributed more to the left or more to the right. In this case, the question asks for the box plot that is skewed left; therefore, determine the box plot where most of the data lies to the right. The box plot that fits this

description is Z.

[pic]

17. The mean of the data set can be found by adding all of the entries together and dividing by the total number of entries. There are 15 total entries in this data set. Add all numbers together, and divide by 15.

|(29 + 30 + 33 + 36 + 41 + 45 + 52 + 52 + 53 + 59 + 60 + 60 + 60 + 60 + 82) ÷ 15 |= |752 ÷ 15 |

| |[pic] |50.133 |

18. A continuous random variable is a random variable that can assume any value in a given interval. When this is the case, the number of possibilities can not be counted.

The number of acorns on an oak tree will always be a positive integer. Even though the number is random, the number is countable. So, this is not a continuous variable.

The number of points scored in a basketball game will always be a positive integer. Even though the number is random, the number is countable. So, this is not a continuous variable.

The number of pages in a book will always be a positive integer. Even though the number is random, the number is countable. So, this is not a continuous variable.

There are an unchanging number of windows in the White House. So, it is not random. It is always the same. So, this is not a random variable.

The speed of a car can take on the value of any real number in a large interval. So, this number is both continuous and random. Therefore, this is a continuous random variable.

19. Find the cumulative frequencies.

|Week |[pic] |[pic] |[pic] |[pic] |

|Frequency |[pic] |[pic] |[pic] |[pic] |

|Cumulative |[pic] |[pic] |[pic] |[pic] |

|Frequency | | | | |

Find the cumulative percentages.

|Week |[pic] |[pic] |[pic] |[pic] |

|Frequency |[pic] |[pic] |[pic] |[pic] |

|Cumulative |[pic] |[pic] |[pic] |[pic] |

|Frequency | | | | |

|Cumulative |[pic] |[pic] |[pic] |[pic] |

|Percentage | | | | |

Plot the weeks and the associated cumulative percentages, using the upper bound for each week category.

[pic]

Connect the plotted points with a curve. The curve represents a continuous function.

[pic]

The ogive curve that represents the frequency table is W.

20. The population being studied is all high school students residing in the state.

In order to assure random selection of a sample population, each high school student that resides in the state must have an equal probability of being selected from the population. There is only one method provided that will meet this criteria.

|V) | |The researcher should randomly select students from all high school students that reside within the state. |

21. It is seen that Adam did not conduct any calls from 12:00 pm to 1 pm; therefore, the histogram is said to contain a gap. Remember that gaps are areas of distribution with no observations.

In order for a histogram to be bimodal or multimodal, the bins of the histogram must form two or more peaks. Even though the given histogram appears to have two peaks, it only has one. Remember that a peak is only formed when the frequency of a histogram changes from increasing to decreasing.

Given the above information, the only true statement is that the histogram is contains a gap.

22. When given a normal distribution graph, the peak represents the mean of the data and the following properties apply.

• About 68% of the data lies within 1 standard deviation of the mean.

• About 95% of the data lies within 2 standard deviations of the mean.

• About 99.8% of the data lies within 3 standard deviations of the mean.

The following graph illustrates these properties.

[pic]

Combining 5th and 6th grade growths will give the following.

[pic]

Comparing this graph with the graph of percentages, calculate the percentage of 5th and 6th graders who grow between 2 inches and 4 inches.

13.5% + 34% = 47.5%

Therefore, the percentage of 5th and 6th graders who grow between 2 inches and 4 inches is 47.5%.

23. Use the equation below to calculate the z-score of a 110 IQ where x represents the score to convert, [pic]represents the average IQ, and s is the standard deviation.

|Z |= |x-[pic] |

| | | |

| | |[pic] |

| | | |

| | |s |

| | | |

| |= |110-100 |

| | | |

| | |[pic] |

| | | |

| | |15 |

| | | |

| |= |10 |

| | | |

| | |[pic] |

| | | |

| | |15 |

| | | |

| |= |0.6666... |

| |[pic] |0.67 |

24. The mode of an ordered data set is the entry seen most frequently. In this case, 60 is the only value used four times, and four is the highest frequency found in the stemplot. The mode is 60.

25. There are three types of experiments.

|Completely Randomized |  -|The completely randomized design is the simplest form of experimental design. In this design, all experimental|

|Design |   |units have an equal probability of receiving any treatments available in the experiments. |

| | | |

|Randomized Block Design |  -|In this design, the experimental units are divided into blocks. Blocks are are subgroups of similar |

| |   |experimental units. Each block is then randomized, and all experimental units within each block have an equal |

| | |probability of receiving any treatments available in the experiments. |

| | | |

|Matched Pairs Design |  -|The matched pairs design is a special type of randomized block design. The design can only be used when there |

| |   |are only two treatments available. Subjects are divided into pairs based on a blocking variable, and each |

| | |experimental unit within the pair is then randomly assigned different treatment options. |

There is random selection with blocking in pairs in the given experiment; therefore, the experiment follows the matched pairs design.

26. There are three characteristics that must be present in order to assure that a survey is well-designed and well-conducted.

|I) | |A sample should be selected to survey. The selected sample should be an accurate representation of the entire population of |

| | |interest. |

| | | |

|II) | |When the sample is selected, it must be randomized. Randomization assures that the sample is an accurate representation of the |

| | |entire population of interest, and it also reduces bias in the survey. |

| | | |

|III) | |When the sample is selected, it must be large enough. Selecting a sample size that is large enough also assures that the sample is |

| | |an accurate representation of the entire population of interest. |

In order for Lydia's survey to be well-designed and well-conducted, she must randomize. The technique that properly assures randomization when selecting a sample to represent the population is as follows:

Lydia should randomly select a sample of students from the entire student population. She should then administer the survey to all of the randomly selected students.

27. In a controlled experiment, the researcher separates the sample population into groups with one group designated as the control group.

All groups are manipulated in some way, except for the control group which remains the same.

28. Symmetry occurs when the entries of the data set are equally distributed on both sides of the median. Determine the box plot where the data is equally distributed on both sides of the median. The box plot that fits this description is W.

[pic]

29. Gaps

Gaps are areas of distribution with no observations.

In the male students' data set, there is no gap or area of distribution without observations.

In the female students' data set, there is a gap in the participation of 1 sport/activity and 2 sports/activities. The data set is, therefore, said to contain a gap.

The data set for the female students possesses a gap.

Mean

The mean of the data set can be found by adding all of the entries together and dividing by the total number of entries. Remember that each dot represents a single entry.

Find the mean of male students' participation. There are 15 total entries in this data set. Add all numbers together, and divide by 15.

|Mean of Male Students' Participation |= |22 ÷ 15 |

| |[pic] |1.467 |

Find the mean of female students' participation. There are 15 total entries in this data set. Add all numbers together, and divide by 15.

|Mean of Female Students' Participation |= |47 ÷ 15 |

| |[pic] |3.133 |

The mean of the male student data is less than the mean of the female student data.

Given the information above, II and III are both true statements.

30. To calculate the probability that a family chosen from this group at random will have 1 child, divide the number of families that had 1 child by the total number of families surveyed.

[pic]

31. When investigating the marginal frequencies of the extracurricular activities, it is seen that athletics is the most popular activity and drama club is the least popular activity.

When investigating the marginal frequencies of the gender of students, it is seen that there is slightly more male involvement than female involvement.

Given the information above, it is seen that I, III, and IV are all true.

32. Symmetry occurs when the entries of the data set are equally distributed on both sides of the median. In this case, the median of the data set is 2. It is seen that the other entries are equally distributed on the left and on the right of the median; therefore, the data set is said to be symmetric. Given that the data set is symmetric, it can not be skewed.

Given the above information, both III and IV are true statements.

33. The mode is the number which occurs most often. The largest number in the frequency column is 7, which corresponds with 7 hours.

A weekly average of 7 hours of singing practice occured 7 times, which is more often than any other average.

Therefore, the mode is 7 hours.

34. The placebo effect occurs when 20% or more of experimental units show a positive response to a placebo. The placebo effect often occurs when experimental units are human participants.

35. Bias is a failure to accurately represent a population in a sample or survey. There are four types of bias.

|Voluntary Response Bias |-|Occurs when participation in a survey is determined by the individuals in the population, yielding a sample |

| | |that is not an accurate representation of the population |

| | | |

|Nonresponse Bias |-|Occurs from a nonresponse to a survey, in which respondents' results greatly differ from nonrespondents' |

| | |results |

| | | |

|Response Bias |-|Occurs from problems with the survey itself, specifically wording issues |

| | | |

|Undercoverage |-|Occurs when members of a population are inadequately represented in a sample population |

The restaurant owner is not accounting for customers who do not have access to the internet; therefore, undercoverage is present.

36. Given that A and B are compound events, use the following formula, defined as the multiplication rule, to find the probability that A and B will occur. Remember that P(B|A) is the probability that B will occur given that A has already occurred.

[pic]

Note: Given that A and B are independent events, the multiplication rule will reduce to the following formula.

[pic]

Define the events.

[pic]

The question asks for the probability that both events occur; therefore, the multiplication rule must be applied.

Rewrite the multiplication rule for the given events, C and R.

[pic]

Calculate P(C) and P(R|C).

Find P(C). There are 34 songs, and 12 of the total songs are country.

[pic]

Find P(R|C). One song has already been selected; therefore, there are 33 songs remaining, and 10 of the total songs are rock.

[pic]

Substitute P(C) and P(R|C) into the multiplication rule formula and simplify to obtain the final answer.

[pic]

37. An independent variable is a variable whose value determines the value of other variables, and it is changed in an experiment to see its effect on other variables.

A variable that changes because of a change in the independent variable is a dependent variable.

In this situation, changing the number of construction workers changes the amount of time it will take to complete the building. However, the height of the building does not change at all.

Therefore, the height of the building is neither an independent nor a dependent variable.

38. In an observational study, the sample population is studied as is. The researcher does not influence the population. Data is gathered and correlations are investigated.

In this situation, it is impossible to perform an experimental study or controlled experiment because a hurricane cannot be artificially generated.

Of the choices given, the best way to investigate the correlation would be through an observational study.

39. To calculate the percentage of females that chose soccer as their favorite sport, find the joint frequency for the number of females that chose soccer. There are 49 females that chose soccer as their favorite sport.

Find the marginal frequency for the total number of females. There are 112 females.

Calculate the percentage of females that chose soccer as their favorite sport.

[pic]

40. To determine the distribution of the sales goals progresses, find the percentages of each category by creating tables.

Create a table for Jim.

Jim's Sales Goal

|Month |1 |2 |3 |4 |5 |6 |

|Percentage |10% |20% - 10% = 10% |50% - 20% = 30% |60% - 50% = 10% |80% - 60% = 20% |100% - 80% = 20% |

The greatest percentage of sales for Jim was in the 3rd month.

Create a table for Bill.

Bill's Sales Goal

|Month |1 |2 |3 |4 |5 |6 |

|Percentage |30% |50% - 30% = 20% |70% - 50% = 20% |80% - 70% = 10% |90% - 80% = 10% |100% - 90% = 10% |

The greatest percentage of sales for Bill was in the 1st month.

The median of Jim's sales goal can be found by locating the bin with the cumulative height of 50 percent. In this case, the bin with the cumulative height of 50 percent is month 3; therefore, Jim met the median of his sales goal in the 3rd month.

The median of Bill's sales goal can be found by locating the bin with the cumulative height of 50 percent. In this case, the bin with the cumulative height of 50 percent is month 2; therefore, Bill met the median of his sales goal in the 2nd month.

The final bin of Jim's Sales Goal cumulative frequency plot has the height of 100, and the final bin of Bill's Sales Goal cumulative frequency plot has the height of 100. Jim and Bill both met their 6 month sales goal.

Given the information above, both I and II are true statements.

41. The situation given in the explanation represents a binomial probability distribution. The best way to calculate the correct answer is to use the following binomial formula.

[pic]

In this equation, n represents the total number of trials, p represents the probability of success, q represents the probability of failure (1 - p), x represents the number of successes in n trials, and n - x represents the number of failures in n trials. Now use this equation to find the probabilities for when x = 3 and x = 4. Then add the probabilities to find the final answer.

[pic]

42. The general form of the linear regression model is as follows.

[pic]

Create a table of values for the household sizes (x) and weekly grocery costs (y) shown on the scatterplot.

|[pic] |[pic] |

|1 |75 |

|2 |75 |

|2 |100 |

|3 |100 |

|3 |150 |

|4 |125 |

|4 |150 |

|5 |175 |

|6 |150 |

|6 |175 |

In order to solve for b0 and b1, find the mean of x, the mean of y, the standard deviation of x, the standard deviation of y, and the correlation coefficient.

The mean of x and y can be found using the formulas below.

[pic]

Using the formula above, find the mean of x.

[pic]

Using the formula above, find the mean of y.

[pic]

Find the standard deviation of x and y. The standard deviation of x and y can be found using the following formulas.

[pic]

Create a table for x-values to assist in the calculation of the standard deviation of x.

|[pic] |[pic] |[pic] |

|1 |-2.6 |6.76 |

|2 |-1.6 |2.56 |

|2 |-1.6 |2.56 |

|3 |-0.6 |0.36 |

|3 |-0.6 |0.36 |

|4 |0.4 |0.16 |

|4 |0.4 |0.16 |

|5 |1.4 |1.96 |

|6 |2.4 |5.76 |

|6 |2.4 |5.76 |

Using the information in the table above and the formula for the standard deviation of x, find the standard deviation of x.

[pic]

Create a table for y-values to assist in the calculation of the standard deviation of y.

|[pic] |[pic] |[pic] |

|75 |-52.5 |2756.25 |

|75 |-52.5 |2756.25 |

|100 |-27.5 |756.25 |

|100 |-27.5 |756.25 |

|150 |22.5 |506.25 |

|125 |-2.5 |6.25 |

|150 |22.5 |506.25 |

|175 |47.5 |2256.25 |

|150 |22.5 |506.25 |

|175 |47.5 |2256.25 |

Using the information in the table above and the formula for the standard deviation of y, find the standard deviation of y.

[pic]

Find the correlation coefficient. The correlation coefficient can be found by using the formula below.

[pic]

Create a table to find the product needed for the correlation coefficient.

|[pic] |[pic] |[pic] |

|-2.6 |-52.5 |136.5 |

|-1.6 |-52.5 |84 |

|-1.6 |-27.5 |44 |

|-0.6 |-27.5 |16.5 |

|-0.6 |22.5 |-13.5 |

|0.4 |-2.5 |-1 |

|0.4 |22.5 |9 |

|1.4 |47.5 |66.5 |

|2.4 |22.5 |54 |

|2.4 |47.5 |114 |

Using the table above, the standard deviation of x, the standard deviation of y, and the formula for the correlation coefficient, find the correlation coefficient.

[pic]

Using the correlation coefficient, the standard deviation of x, the standard deviation of y, and the formula for b1, calculate b1.

[pic]

Using the mean of x, the mean of y, b1, and the formula for b0, find b0.

[pic]

Substitute b0 and b1 into the general form of the linear regression model to obtain the final answer.

[pic]

The numbers found here may be slightly different than those found using a calculator due to rounding.

43. The upper 25 percent of the female box plot is contained between 1000 to 1200; therefore, about 25 percent of female students use 1000 to 1200 cellular minutes a month.

The lower 25 percent of the male box plot is contained between 300 to 400; therefore, about 25 percent of male students use 300 to 400 cellular minutes a month.

The median of the box plots are the middle values. The median number of cellular minutes used by female students is 900, and the median number of cellular minutes used by male students is 500. The median of female cell phone minute usage is greater than the median of male cell phone usage.

The interquartile range of each box plot can be found by subtracting the first quartile value from the third quartile value for each box plot.

|IQR of Female Students' Monthly Cell Phone Usage | =  |1000 - 800 = 200 |

| | | |

|IQR of Male Students' Monthly Cell Phone Usage | =  |700 - 400 = 300 |

The interquartile range of female cell phone minute usage is less than the interquartile range of male cell phone minute usage.

Given the information above, statements II and III are true.

44. In this case, 30 forms the left side of the box; therefore, it represents the first quartile of the data. Only about 25 percent of the data lies to the left of the first quartile.

Swimming Competition Finshing Times

[pic]

Time (seconds)

Given the information above, it is seen that 25 percent of the swimmers completed the competition in less than 30 seconds.

45. Given events A and B, use the following formula, defined as the addition rule, to find the probability that A or B will occur.

[pic]

Define the events.

[pic]

The question asks for the probability that either event occurs; therefore, the addition rule must be applied.

Rewrite the addition rule for the given events, B and S.

[pic]

Calculate P(B), P(S), and P(B [pic]S).

Find P(B). There are 15 total shirts in the closet, and 8 of the shirts are blue.

[pic]

Find P(S). There are 15 total shirts in the closet, and 9 of the total shirts have stripes.

[pic]

Find P(B [pic]S). There are 15 total shirts in the closet, and there are 5 shirts that are blue and have stripes.

[pic]

Substitute P(B), P(S), and P(B [pic]S) into the addition rule formula and simplify to obtain the final answer.

[pic]

46. Upon observation of the bins of the adults and exercise histogram, it is seen that the bins form two peaks; therefore, the data is said to be bimodal. Given that the data set is bimodal, it can not be unimodal or multimodal.

It is seen that the entries of the adults and exercise histogram are equally distributed on the left and on the right of the median; therefore, the data set is said to be symmetric. Given that the data set is symmetric, it can not be skewed.

Given the above information, both II and III are true.

47. A scatterplot with positive correlation is similar to a line with a positive slope. A scatterplot with data running from the lower left of the plot to the upper right of the plot is said to have a positive correlation; therefore, the answer is Z.

[pic]

48. Arrange the numbers from smallest to largest; the median is the value in the middle of the set, $9,100.

49. There are three types of experiments.

|Completely Randomized |  -|The completely randomized design is the simplest form of experimental design. In this design, all experimental|

|Design |   |units have an equal probability of receiving any treatments available in the experiments. |

| | | |

|Randomized Block Design |  -|In this design, the experimental units are divided into blocks. Blocks are are subgroups of similar |

| |   |experimental units. Each block is then randomized, and all experimental units within each block have an equal |

| | |probability of receiving any treatments available in the experiments. |

| | | |

|Matched Pairs Design |  -|The matched pairs design is a special type of randomized block design. The design can only be used when there |

| |   |are only two treatments available. Subjects are divided into pairs based on a blocking variable, and each |

| | |experimental unit within the pair is then randomly assigned different treatment options. |

There is random selection with blocking in pairs in the given experiment; therefore, the experiment follows the matched pairs design.

50. It is seen that the entries of the school enrollment histogram are equally distributed on the left and on the right of the median; therefore, the data set is said to be symmetric. Given that the data set is symmetric, it can not be skewed.

It is also seen that the bins of the histogram are equal in height; therefore, the school enrollment histogram is said have a uniform distribution. Given that the data set has a uniform distribution, it does not have a mode; therefore, the data set can not be unimodal, bimodial, or multimodal.

Given the above information, both IV and V are true.

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