Mathematics 243, Lewis



Mathematics 243, Rob Lewis

Final Exam Practice Problems

Part I

Fill in the blank.

1. A college counselor observes people waiting for the bus and records whether they are sitting alone or not.

Identify: a) the individual b) the variable c) type of variable

________________ _______________ __________________

2. Students are given a tennis ball and asked to throw it as far as possible. The distance it goes is recorded.

Identify: a) the individual b) the variable c) type of variable

________________ _______________ __________________

3. If a distribution is skewed to the right what can you say about the mean and median?

4. An extreme outlier is added to the data what statistical measurement changes most?

5. What is the standard deviation of a standard normal distribution:

6. On a particular statistics final exam, the maximum number of points a student could earn was 200. Here is a sample of student test scores from the class:

121, 142, 118, 179, 146, 133, 124, 128, 137, 116

a. Use a ruler to draw an accurate boxplot of the data. Label each component and its numerical value. For example, label the location of Q3 and its value.

b. Use the Interquartile Range to test for outliers. Are there any? Explain briefly.

7. Six students were asked how many classes they missed in all their courses last term. The results are shown in a list below. Calculate the mean and record below the data. Demonstrate how to calculate the standard deviation “by hand” , i.e using the formula.

X

12

11

8

12

5

6

[pic] [pic]

8. On the normal distribution provided, label the mean, plus/minus 1 standard deviation, plus/minus 2 standard deviations, and plus/minus 3 standard deviations.

For the next three problems use the following information. Suppose the Print-Rite Company is interested in the number of continuous hours their printers will operate before mechanical failure. Previous sampling has shown that the data follows a normal distribution (bell curve shape histogram) with a mean of 280 hours and a standard deviation of 18 hours.

9. What percent of the printers will last between 250 and 270 hours? Shade in the appropriate area.

10. Suppose the number of hours the printer last before failure is N(300, 22). Calculate: P( X < 340). Shade in the appropriate area.

11. Provide a reasonable five-number summary of the length of time the printers will last assuming the mean is 280 hours with standard deviation 18 hours. You are not required to use the normal graph below.

|Measurement |Value |

| | |

| | |

| | |

| | |

| | |

12. My son, Jimmy, is practicing his target shooting with a sling shot. Out of 30 attempts he hit his target 9 times. Before his next shot he tells me that he as 0.30 probability of hitting the target with his next shot. This is an example of what type of probability?

13. I watch my son hit the target 9 times out of 30. I think he has a higher probability of 0.40 of hitting the target. This is an example of what type of probability?

14. Jordon is interested in how long it takes people to find a parking spot at LBCC between 8 am and 2 pm. He randomly samples 5 cars every hour starting at 8 am and records the driver’s gender and how long they take to park. What type of study is this?

Voluntary Experiment Survey Observational None of the above

15. Jordon is interested in how long it takes people to find a parking spot at LBCC between 8 am and 2 pm. Starting at 8 am he selects every fifth car entering the parking lot. What type of sampling is he using?

Convenience Voluntary SRS Systematic Cluster Stratified

16. Jordon is interested in how long it takes people to find a parking spot at LBCC between 8 am and 2 pm. He randomly samples 5 cars every hour starting at 8 am. What type of sampling is he using?

a. Convenience

b. Voluntary

c. SRS

d. Systematic

e. Cluster

f. Stratified

17. Jordon is interested in how long it takes people to find a parking spot at LBCC between 8 am and 2 pm. He places a survey form on each car window asking the driver to record the amount of time it takes them to park the next day and to return the form to a collection box in Takena Hall. What type of sampling is this?

a. Convenience

b. Voluntary

c. SRS

d. Systematic

e. Cluster

f. Stratified

18. A probability model with a finite sample space is a __________________ probability model. A probability model which assigns probabilities as the area under a density curve is a __________________ probability model.

19. (8 pts) The United States Census of all citizens reported the average number of children under age 18 per household is 2.4 with standard deviation 0.8. A study consisting of a random sample of 50 Oregonians reported the average number of children is 2.1 with standard deviation 1.2.

Identify whether the value is a parameter or statistic, and its symbol.

|Value |Parameter or Statistic |Symbol |

|50 | | |

|2.1 | | |

|0.8 | | |

|2.4 | | |

20. (16 pts) An industrial psychologist is interested in studying the effect of room temperature and humidity on the performance of tasks requiring manual dexterity. She chooses three temperatures of 65 degrees Fahrenheit, 80 degrees Fahrenheit and 95 degrees Fahrenheit with humidity of 60% and 80%. She plans to measure the number of correct insertions, during a 15-minute period using a peg-and-hole apparatus requiring the use of both hands simultaneously. After each subject is trained on the apparatus, he or she is asked to make as many insertions as possible in a 15-minute period. Sixty factory workers from each of three different companies are to be randomly assigned to the different temperature and humidity combinations.

a. Identify the population under study.

b. Identify the “individuals” units in this experiment.

c. What are the factors?

d. How many treatments are there? Specify two of these treatments.

e. What blocking variable(s) are reasonable? Why?

f. What is the response variable?

21. (24 pts) Assume the weights of oranges at the grocery store follow approximately a normal distribution with mean 7.5 oz and standard deviation 2.1 oz.

a. What is the probability of selecting 9 oranges with a mean weight between 7.5 oz and 8.5 oz? Show your work using the proper notation. Shade in the area under the normal curve correctly.

b. What is the probability of selecting 9 oranges with a mean weight less than 6.5 oz? Show your work using the proper notation. Shade in the area under the normal curve correctly.

c. What is the probability of a single randomly selected orange having a weight between 7.5 oz and 8.5 oz ? Show your work using the proper notation. Shade in the area under the normal curve correctly.

d. Complete this statement: “The probability of a random sample of 25 oranges falling between _______ and _______ is 0.95. “ Show your work.

Part II.

1. Three stellar stats researchers independently select random samples from the same population. The sample sizes are 1000 for Sarah, 4000 for Lewis, and 250 for TJ. Each researcher constructs a 95% confidence interval. Match the following margins of error with the correct researcher: 0.015 0.031 .062

2. Julie selects 100 subjects at random from a population, observes 50 successes, and calculates three confidence intervals. The confidence levels are 90%, 95%, and 99%. Match the each confidence interval below with the confidence level:

(.402,.598) (.371,.629) (.418,.582)

3. Explain:Teagan reports in her study about the effect of new drug to improve recovery rates of stroke victims a p-value of 0.0351. She decides to “reject the null hypothesis”. James says no way. Who is right? Explain.

4. Vanessa reports in her study a p-value of 0.042 and a confidence interval for the difference between the average reaction time of men and women. Circle the confidence interval(s) below that would have been possible in her study.

95% Confidence Interval: (-2.2, 10.2)

95% Confidence Interval: (1.1, 13.1)

99% Confidence Interval: (-3.2, 12.6)

99% Confidence Interval: (0.4, 15.8)

5. Child psychologist, Dr. Porter reports that children ages 2-3 will spend on average 3.4 hours per day by themselves in a day care environment. Her mean was based on a sample of 49 children and had a standard deviation of 4.8 hours. She reported a confidence interval of (2.3 , 4.5).

a) What was the standard error of the mean? ____________________

b) What was the margin of error? _____________________________

c) What was the confidence level? ____________________________

d) What was the value of (? _________________________________

e) Name two actions she could take to decrease the margin of error.

6. Health advocate Wes volunteers his time to test homes in her hometown for excessive lead dust. Lead dust is known to cause learning disabilities in children and is found in older homes where lead paint has been used. In a random survey of the area he found that 300 homes out of 450 had excessive levels of lead dust.

a) What is the experimental unit? ___________

b) What is the variable? _________________________

c) What is the symbol of the parameter being estimated? _____________________

d) What does this parameter represent in the context of this problem?

e) What is the symbol for the sample statistic? ______________________________

f) What is the value of the sample statistic? ________________________________

g) Report your results using a 99% complete confidence interval statement.

7. ODOT engineers Sawyers and Salinas did a small pilot study of the Highway 99 and Oakville Road intersection. They wrote down the following times in seconds between when a car turns onto Oakville Road and a car on Highway arrives at the intersection:

0.6 1.3 2.8 .4 .8 5.1 1.2 1.1 5.4 .5 1.0 3.2

a) What is the experimental unit? ___________

b) What is the variable under study? _________________________

c) What is the symbol of the parameter being estimated? ________________

d) What does this parameter represent in the context of this problem?

e) What is the symbol for the sample statistic? ______________

f) What is the value of the sample statistic? _______________

g) Report your results using a complete 95% confidence interval statement.

8. The new director of the LBCC nursing school, Dr. W, is concerned with the percentage of students who successfully complete the nursing program. He wonders how the 66% success rate at LBCC compares with other schools in the region. He hires statistical consultant, Dr. Mu, to randomly survey 1200 entering students from nursing schools across Oregon, Washington, and California. Dr. Mu reports that only 550 of these students successfully complete their nursing program.

In Words Mathematically

Ho:___________________________________________ Ho: ___________

___________________________________________

HA:___________________________________________ HA: ___________

___________________________________________

9. Senator Margie O’Error was elected based largely on her efforts to increase funding for mathematics education in the United States. As a result of smaller classroom size and better-trained teachers, she believes that American children now might be performing at a higher level in mathematics than European children of the same age.

In Words Mathematically

Ho:___________________________________________ Ho: ___________

HA:___________________________________________ HA: ___________

10. Ms. Creel is concerned about her 4000 employees taking excessive amounts of sick leave. She reads in a business journal that the nationwide average number of sick days per person is 4.58 days per year. She analyzes a random sample of 20 employee records. She records a sample mean of 8.12 days per year and a sample standard deviation of 8.34 days per year.

In Words Mathematically

Ho:___________________________________________ Ho: ___________

HA:___________________________________________ HA: ___________

11. Safety racing engineer Dr. Lee Sigma designs a device which projects a red color on your windshield in front of you when your car is approaching another car too quickly, i.e. you need to brake! He hopes that the extra visual aide will reduce the amount of time it takes for the car to stop. He records the stopping distances of 35 drivers using a normal car. He then measures the stopping distance, at the same speed, for the same 35 drivers driving the same car outfitted with the visual aide device.

In Words Mathematically

Ho:___________________________________________ Ho: ___________

HA:___________________________________________ HA: ___________

12. Analyze question #8 and #10

a) What is your “decision” based on your p-value?

b) What conclusion would you draw?

13. Based on a random sample of four hundred fifty tacks we are _____% confident that the true proportion of tacks that will land face up when dropped from a height of five feet is between .26 and .34.

a. What is [pic]?

b. What is the margin of error?

c. What confidence level was used? (No guesses, show your work!)

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