Chapter 1 Review



Chapter 1 Review – Answer Key

Multiple Choice

1. A zoologist studying adult bears measures a number of different variables. Which of the following possible variables is categorical?

A. The weight in pounds of an adult bear

B. The level of aggression (low, moderate, high) displayed by an adult bear

C. The number of fish an adult bear eats in a particular day

D. The age of an adult bear in years

E. The number of children an adult bear has per year.

2. If the largest value of a data set is doubled, which of the following is not true?

A. The mean increases.

B. The standard deviation increases.

C. The interquartile range increases.

D. The range increases.

E. The median remains unchanged.

3. The stem-and-leaf diagram below gives the distribution of the ages in years of 20 participants at a family reunion.

[pic]

4. Which of the following distributions are more likely to be skewed to the right than skewed to the left?

I. Household incomes

II. Home prices

III. Ages of teenage drivers

A. II only B. I and II C. I and III D. II and III E. I, II and III

5. If the standard deviation of a set of observations is 0, you can conclude:

A. That there is no relationship between the observations

B. That the average value is 0

C. That all observations are the same value

D. That a mistake in arithmetic has been made

E. None of the above

6. A 1995 poll by the Program for the International Policy asked respondents what percentage of the United States budget they thought went to foreign aid. The mean response was 12% and the median was 15%. (The actual amount is less than 1%). What do these responses indicate about the likely shape of the distribution of all the responses?

A. The distribution is skewed to the left

B. The distribution is skewed to the right

C. The distribution is symmetric

D. The distribution is bell-shaped with a standard deviation of 3%

E. The distribution is uniform between 15% and 18%

7. In which of the following situations would a pie chart be an appropriate graph to use to summarize your data?

A. You want to display the distribution of favorite Coke product for the students in your statistics class.

B. You are giving a talk on "the decay of the American family" and want to show in a graph how the number of divorces in American marriages has increased between 1960 and 1998.BC.

C. You want to compare the life expectancies of different professions by displaying and comparing graphs of ages at death for random samples of famous scientists, authors, actors, and politicians.

8. From the side-by-side boxplots shown below, which of the following statements is true? Note that data set 1 corresponds to "var1" on the vertical axis and data set 2 corresponds to "var2" on the vertical axis.

[pic]

A. The IQR of data set 1 is smaller than that of data set 2.

B. The range of data set 1 is larger than that of data set 2.

C. The median of data set 1 is larger than that of data set 2.

D. 50% of the data in set 1 is less than 15.

E. The mean of set 2 is less than the mean of set 1.

9. The mean birth weight of infants born at a certain hospital in the month of April was 128 oz. with a standard deviation of 10.2 oz. Which of the following is a correct interpretation of standard deviation?

A. All the infants born in April weighed between 117.8 oz. and 138.2 oz.

B. About half the infants born in April weighed between 117.8 oz. and 138.2 oz.

C. The difference between the mean weight and the median weight of infants born in April was 10.2 oz.

D. The distance between the weight of each infant bon in April and the mean weight was, on average, about 10.2 oz.

E. The mean weight of infants born in subsequent months is likely to be within 10.2 oz. of the mean weight in April.

10. A medical researcher collects health data on many women in each of several countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of adult women in one of the countries.

Country A: 92, 110, 120, 160, 240

About what percent of Country A women weigh between 110 and 240 pounds?

A. 50%

B. 65%

C. 75%

D. 85%

E. 95%

Free Response

11. The back-to-back stemplot shows the lifetimes of several Brand X and Brand Y batteries in hours.

[pic]

a) What is the longest that any battery lasted?

55 hours

b) Using your calculator, find the five number summary for both sets of data. Construct a comparative box and whisker plot for both sets of data.

Brand X Brand Y

Min 30 17

Q1 32 42

Q2 39 43

Q3 42 48

Max 55 50

c) Are there any outliers? Justify your answer mathematically for both Brand X and Brand Y.

Brand X: None Brand Y: 17, 22, 26

1.5(10) = 15 1.5(6) = 9

42 + 15 = 57 48 + 9 = 57

32 – 15 = 17 42 – 9 = 33

d) Give one reason that someone might prefer Brand X. Give another reason why someone might prefer Brand Y.

Brand X has the longest lasting battery. Brand Y is more consistently higher.

12. Below are dotplots for three small datasets: A, B, and C. Without performing any calculations, rank the standard deviations of the datasets from lowest to highest. Justify your answer.

[pic]

C, A, B

13. Do people’s opinion of the alt-rock band Coastal Surface depend on their age? Here are some data that address this question.

| |11 – 14 years |15 – 18 years |19 – 22 years |Total |

|Like |18 |38 |40 |96 |

|Dislike |30 |10 |67 |107 |

|Uncertain |15 |17 |15 |47 |

|Total |63 |65 |122 |250 |

a) Calculate the marginal distribution of ages in percents.

11 – 14: 0.25 15 – 18: 0.26 19 – 22: 0.49

b) Calculate the conditional distributions for opinion of the band based on age group. You may present your results in either a table or a graph.

| |11 – 14 years |15 – 18 years |19 – 22 years |

|Like |.29 |.58 |.33 |

|Dislike |.48 |.15 |.55 |

|Uncertain |.24 |.26 |.12 |

c) Do you believe that there is an association between opinion of the band and age? Justify your response.

Yes, 15 – 18 year olds are more likely to “Like” the band, whereas 11 – 14 and 19 – 22 year olds are more likely to “Dislike” the band.

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Which of the following statements about the distribution is correct?

A. The mean is larger than the median.

B. The distribution is strongly skewed to the left.

C. The mean is equal to the median.

D. It makes the most sense to use the mean and standard deviation as a numerical summary of the center and spread of this distribution.

E. The mean is less than the median.

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