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49 . You conduct a study, based on a sample drawn from a normally distributed population with a known variance, with the following hypotheses:
H
_{0} :
μ ≥ 35.5
H
_{a} :
μ <35.5
Will you conduct a one-tailed or two-tailed test?
Use the following information to answer the next three exercises. Nationally, 80 percent of adults own an automobile. You are interested in whether the same proportion in your community own cars. You draw a sample of 100 and find that 75 percent own cars.
50 . What are the null and alternative hypotheses for this study?
51 . What test will you use, and why?
52 . You conduct a poll of political opinions, interviewing both members of 50 married couples. Are the groups in this study independent or matched?
53 . You are testing a new drug to treat insomnia. You randomly assign 80 volunteer subjects to either the experimental (new drug) or control (standard treatment) conditions. Are the groups in this study independent or matched?
54 . You are investigating the effectiveness of a new math textbook for high school students. You administer a pretest to a group of students at the beginning of the semester, and a posttest at the end of a year’s instruction using this textbook, and compare the results. Are the groups in this study independent or matched?
Use the following information to answer the next two exercises. You are conducting a study of the difference in time at two colleges for undergraduate degree completion. At College A, students take an average of 4.8 years to complete an undergraduate degree, while at College B, they take an average of 4.2 years. The pooled standard deviation for this data is 1.6 years
55 . Calculate Cohen’s d and interpret it.
56 . Suppose the mean time to earn an undergraduate degree at College A was 5.2 years. Calculate the effect size and interpret it.
57 . You conduct an independent-samples t-test with sample size ten in each of two groups. If you are conducting a two-tailed hypothesis test with α = 0.01, what p-values will cause you to reject the null hypothesis?
58 . You conduct an independent samples
t -test with sample size 15 in each group, with the following hypotheses:
H
_{0} :
μ ≥ 110
H
_{a} :
μ <110
If
α = 0.05, what
t -values will cause you to reject the null hypothesis?
Use the following information to answer the next six exercises. College students in the sciences often complain that they must spend more on textbooks each semester than students in the humanities. To test this, you draw random samples of 50 science and 50 humanities students from your college, and record how much each spent last semester on textbooks. Consider the science students to be group one, and the humanities students to be group two.
59 . What is the random variable for this study?
60 . What are the null and alternative hypotheses for this study?
61 . If the 50 science students spent an average of $530 with a sample standard deviation of $20 and the 50 humanities students spent an average of $380 with a sample standard deviation of $15, would you not reject or reject the null hypothesis? Use an alpha level of 0.05. What is your conclusion?
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