Question 9.1

Question 9.2

Question 9.3

Question 9.4

239

Question 9.5

Question 9.6

Question 9.7

Question 9.8

Question 9.9

Question 9.10

Question 9.11

Question 9.12

We use formulas to describe calculations. Find the error in each of the following formulas. Explain why each is incorrect and provide a correction.

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Question 9.13

For the data 93, 97, 91, 88, 103, 94, 97, calculate the standard deviation under both of these conditions:

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Question 9.14

For the data 1.01, 0.99, 1.12, 1.27, 0.82, 1.04, calculate the standard deviation under both of the following conditions. (Note: You will have to carry some calculations out to the third decimal place to see the difference in calculations.)

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Question 9.15

Identify the critical t value in each of the following circumstances:

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Question 9.16

Calculate degrees of freedom and identify the critical t value for a single-sample t test in each of the following circumstances:

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Question 9.17

Identify the critical t values for each of the following tests:

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Question 9.18

Assume we know the following for a two-tailed, single-sample t test, at a p level of 0.05: μ = 44.3, N = 114, M = 43, s = 5.9.

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Question 9.19

Assume we know the following for a two-tailed, single-sample t test: μ = 7, N = 41, M = 8.5, s = 2.1.

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Question 9.20

Students in a statistics course reported the number of hours of sleep they get on a typical weeknight. These data appear below.

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Question 9.21

The relation between the z distribution and the t distributions: For each of the problems described below, which are the same as some of those described in Exercise 9.17, identify what the critical z value would have been if there had been just one sample and we knew the mean and standard deviation of the population:

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240

Question 9.22

t statistics and standardized tests: On its Web site, the Princeton Review claims that students who have taken its course improve their Graduate Record Examination (GRE) scores, on average, by 210 points. (No other information is provided about this statistic.) Treating this average gain as a population mean, a researcher wonders whether the far cheaper technique of practicing for the GRE on one’s own would lead to a different average gain. She randomly selects five students from the pool of students at her university who plan to take the GRE. The students take a practice test before and after 2 months of self-study. They reported (fictional) gains of 160, 240, 340, 70, and 250 points. (Note that many experts suggest that the results from self-study are similar to those from a structured course for students who have the self-discipline to study on their own. Regardless of the format, preparation has been convincingly demonstrated to lead to increased scores, on average.)

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Question 9.23

Single-sample t test, military training, and anger: Bardwell, Ensign, and Mills (2005) assessed the moods of 60 male U.S. Marines following a month-long training exercise conducted in cold temperatures and at high altitudes. Negative moods, including fatigue and anger, increased substantially during the training and lasted up to 3 months after the training ended. Mean mood scores were compared to population norms for three groups: college men, adult men, and male psychiatric outpatients. Let’s examine anger scores for six Marines at the end of training; these scores are fictional, but their mean and standard deviation are very close to the actual descriptive statistics for the sample: 14, 12, 13, 12, 14, 15.

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Question 9.24

Consideration of Future Consequences and a dot plot: The following data are Consideration of Future Consequences (CFC) scores for 20, already arranged in order from lowest to highest:

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Question 9.25

Credit card debt and dot plots: Below are the amounts of credit card debt reported by 27 men and 23 women.

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Question 9.26

Paid days off and the single-sample t test: The number of paid days off (e.g., vacation, sick leave) taken by eight employees at a small local business is compared to the national average. You are hired as a consultant by the new business owner to help her determine how many paid days off she should provide. In general, she wants to set some standard for her employees and for herself. Let’s assume your search on the Internet for data on paid days off leaves you with the impression that the national average is 15 days. The data for the eight local employees during the last fiscal year are: 10, 11, 8, 14, 13, 12, 12, and 27 days.

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Question 9.27

Death row and the single-sample t test: The Florida Department of Corrections publishes an online death row fact sheet. It reports the average time on death row prior to execution as 11.72 years but provides no standard deviation. This mean is a parameter because it is calculated from the entire population of executed prisoners in Florida. Has the time spent on death row changed in recent years? According to the execution list linked to the same Web site, the six prisoners executed in Florida during the years 2003, 2004, and 2005 spent 25.62, 13.09, 8.74, 17.63, 2.80, and 4.42 years on death row, respectively. (All were men, although Aileen Wuornos, the serial killer portrayed by Charlize Theron in the 2003 film Monster, was among the three prisoners executed by the state of Florida in 2002; Wuornos spent 10.69 years on death row.)

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