# Topic 4 exercises

• Chapter 10, numbers 10.9, 10.10, 10.11, and 10.12
• Chapter 11, numbers 11.11, 11.19, and 11.20
• Chapter 12, numbers 12.7, 12.8, and 12.10

10.9 The normal range for a widely accepted measure of body size, the body mass index (BMI), ranges from 18.5 to 25. Using the midrange BMI score of 21.75 as the null hypothesized value for the population mean, test this hypothesis at the .01 level of significance given a random sample of 30 weight-watcher participants who show a mean BMI = 22.2 and a standard deviation of 3.1.

10.10 Let’s assume that, over the years, a paper and pencil test of anxiety yields a mean score of 35 for all incoming college freshmen. We wish to determine whether the scores of a random sample of 20 new freshmen, with a mean of 30 and a standard deviation of 10, can be viewed as coming from this population. Test at the .05 level of significance.

10.11 According to the California Educational Code (http://www.cde.ca.gov/ls/fa/sf/pegui-demidhi.asp), students in grades 7 through 12 should receive 400 minutes of physical education every 10 school days. A random sample of 48 students has a mean of 385 minutes and a standard deviation of 53 minutes. Test the hypothesis at the .05 level of significance that the sampled population satisfies the requirement.

10.12 According to a 2009 survey based on the United States census (http://www.census.gov/prod/2011pubs/acs-15.pdf), the daily one-way commute time of U.S. workers averages 25 minutes with, we’ll assume, a standard deviation of 13 minutes.

An investigator wishes to determine whether the national average describes the mean commute time for all workers in the Chicago area. Commute times are obtained for a random sample of 169 workers from this area, and the mean time is found to be 22.5 minutes. Test the null hypothesis at the .05 level of significance.

11.11 Give two reasons why the research hypothesis is not tested directly.

11.19 How should a projected hypothesis test be modified if you’re particularly concerned about (a) the type I error? (b) the type II error?

11.20 Consult the power curves in Figure 11.7 to estimate the approximate detection rate, rounded to the nearest tenth, for each of the following situations: (a) a four-point effect, with a sample size of 13 (b) a ten-point effect, with a sample size of 29 (c) a seven-point effect with a sample size of 18 (Interpolate) (I ATTACHED FIGURE 11.7)

*12.7 In Question 10.5 on page 191, it was concluded that, the mean salary among the population of female members of the American Psychological Association is less than that (\$82,500) for all comparable members who have a doctorate and teach full time. (a) Given a population standard deviation of \$6,000 and a sample mean salary of \$80,100 for a random sample of 100 female members, construct a 99 percent confidence interval for the mean salary for all female members (b) Given this confidence interval, is there any consistent evidence that the mean salary for all female members falls below \$82,500, the mean salary for all members?

12.8 In Review Question 11.12 on page 218, instead of testing a hypothesis, you might prefer to construct a confidence interval for the mean weight of all 2-pound boxes ofcandy during a recent production shift. (a) Given a population standard deviation of .30 ounce and a sample mean weight of 33.09 ounces for a random sample of 36 candy boxes, construct a 95 percent con-fidence interval (b) Interpret this interval, given the manufacturer’s desire to produce boxes of candy that, on the average, exceed 32 ounces.

12.10 Imagine that one of the following 95 percent confidence intervals estimates the effect of vitamin C on IQ scores:

95% CONFIDENCE INTERVAL LOWER LIMIT UPPER LIMIT

1100102

29599

3102106

490 111

59198

(a) Which one most strongly supports the conclusion that vitamin C increases IQ scores?

(b) Which one implies the largest sample size?

(c) Which one most strongly supports the conclusion that vitamin C decreases IQ scores?

(d) Which one would most likely stimulate the investigator to conduct an additional experiment using larger sample sizes?