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62 . What would be your decision, if you were using α = 0.01?
Use the information to answer the next six exercises. You want to know if proportion of homes with cable television service differs between Community A and Community B. To test this, you draw a random sample of 100 for each and record whether they have cable service.
63 . What are the null and alternative hypotheses for this study
64 . If 65 households in Community A have cable service, and 78 households in community B, what is the pooled proportion?
65 . At α = 0.03, will you reject the null hypothesis? What is your conclusion? 65 households in Community A have cable service, and 78 households in community B. 100 households in each community were surveyed.
66 . Using an alpha value of 0.01, would you reject the null hypothesis? What is your conclusion? 65 households in Community A have cable service, and 78 households in community B. 100 households in each community were surveyed.
Use the following information to answer the next five exercises. You are interested in whether a particular exercise program helps people lose weight. You conduct a study in which you weigh the participants at the start of the study, and again at the conclusion, after they have participated in the exercise program for six months. You compare the results using a matched-pairs t-test, in which the data is {weight at conclusion – weight at start}. You believe that, on average, the participants will have lost weight after six months on the exercise program.
67 . What are the null and alternative hypotheses for this study?
68 . Calculate the test statistic, assuming that ${\overline{x}}_{d}$ = –5, s _{d} = 6, and n = 30 (pairs).
69 . What are the degrees of freedom for this statistic?
70 . Using α = 0.05, what is your decision regarding the effectiveness of this program in causing weight loss? What is the conclusion?
71 . What would it mean if the t -statistic had been 4.56, and what would have been your decision in that case?
72 . What is the mean and standard deviation for a chi-square distribution with 20 degrees of freedom?
Use the following information to answer the next four exercises. Nationally, about 66 percent of high school graduates enroll in higher education. You perform a chi-square goodness of fit test to see if this same proportion applies to your high school’s most recent graduating class of 200. Your null hypothesis is that the national distribution also applies to your high school.
73 . What are the expected numbers of students from your high school graduating class enrolled and not enrolled in higher education?
74 . Fill out the rest of this table.
Observed ( O ) | Expected ( E ) | O – E | ( O – E )2 | $\frac{{(O-E)}^{2}}{z}$ | |
---|---|---|---|---|---|
Enrolled | 145 | ||||
Not enrolled | 55 |
75 . What are the degrees of freedom for this chi-square test?
76 . What is the chi-square test statistic and the p -value. At the 5% significance level, what do you conclude?
77 . For a chi-square distribution with 92 degrees of freedom, the curve _____________.
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