9.7 Define the sampling distribution of the mean.
9.8 Specify three important properties of the sampling distribution of the mean.
9.9 If we took a random sample of 35 subjects from some population, the associated s
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9.7 Define the sampling distribution of the mean.
9.8 Specify three important properties of the sampling distribution of the mean.
9.9 If we took a random sample of 35 subjects from some population, the associated sampling distribution of the mean would have the following properties (true or false).
9.13 Given a sample size of 36, how large does the population standard deviation have to be in order for the standard error to be
9.14 (a) A random sample of size 144 is taken from the local population of grade-school children. Each child estimates the number of hours per week spent watching TV. At this point, what can be said about the sampling distribution?
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 mid-range 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 5 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 deter-mine 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/peguidemidhi.asp ), students in grades 7–12 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 REVIEW QUESTIONS 235sample 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.
The first reason that the hypothesis is not tested directly is that is does not have the necessary precision to be tested. A hypothesis must specify a single number about which the hypothesized sampling distribution can be generated. The second reason the hypothesis is not tested directly is that the research hypothesis is identified with the alternative hypothesis. The decision to reject the null hypothesis is made provided that there is strong support for the research hypothesis. The decision to retain the null hypothesis is made when there is weak support for the null hypothesis (Witte and Witte, 2017).
11.19 How should a projected hypothesis test be modified if you’re particularly concerned about
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:
12.7 In Question 10.5 on page 231, 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.
12.8 In Review Question 11.12 on page 263, instead of testing a hypothesis, you might prefer to construct a confidence interval for the mean weight of all 2-pound boxes of candy during a recent production shift.
12.10 Imagine that one of the following 95 percent confidence intervals estimates the effect of vitamin C on IQ scores:
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