Multiple_Choice_9.1-9.3_no_answers-2

Sections 9.1 - 9.3 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. A marriage counselor claims that the divorce rate in the United States is 30%. She would like to determine if the divorce rate is greater among couples from the United States that have children within the first two years of marriage . Let p = the true proportion of all couples that have children within the first two years of marriage that get divorced. Which one of the following sets of hypotheses is appropriate? a. H 0 : = 0.3; H a : ¹ 0.3 b. H 0 : = 0.3; H a :  0.3 c. H 0 : p > 0.3; H a : p  0.3 d. H 0 : p = 0.3; H a : p  0.3 e. H 0 : p = 0.3; H a : p  0.3 ____ 2. In a statistical test of hypotheses, we say the data are statistically significant at level  if a.  = 0.05. b.  is small. c. the P -value is less than  . d. the P -value is larger than  . e. the sample statistic resulting from the data is more than two standard deviations away from the mean. ____ 3. A university administrator obtains a random sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes ( P = 0.287). Which of the following is a correct interpretation of this value? a. The GPAs for male and female scholarship athletes are identical, except for 28.7% of the athletes. b. The maximum difference in GPAs between male and female scholarship athletes is 0.287. c. If in fact there is no difference in mean GPAs, there is a 0.287 probability of getting a difference in GPAs between male and female scholarship athletes as large as that observed in the sample by chance in a random sample from this population. d. The chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in GPAs is 0.287. e. The probability that female athletes have higher GPAs than males do is 0.287. ____ 4. I conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level  = 0.05. I may conclude that a. the test would also be significant at level  = 0.10. b. the test would also be significant at level  = 0.01. c. the P -value is less than 0.05. d. both (a) and (c) are true. e. both (b) and (c) are true. ____ 5. A test of significance produces a P -value of 0.024. Which of the following conclusions is appropriate? a. Accept H a at the  = 0.05 level b. Reject H a at the  = 0.01 level c. Accept H 0 at the  = 0.01 level d. Reject H 0 at the  = 0.05 level e. Fail to reject H 0 at the  = 0.05 level

____ 6. If we reject the null hypothesis when, in fact, it is true, we have a. committed a Type I error. b. committed a Type II error. c. a probability of being correct that is equal to the P -value. d. a probability of being correct that is equal to 1 – P -value. e. set the  level too high. ____ 7. A researcher plans to conduct a test of hypotheses at the  = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. What is the probability that the researcher will commit a Type I error? a. 0.01 b. 0.10 c. 0.89 d. 0.90 e. The probability of making a Type I error is equal to the P -value. ____ 8. When a customer has a drier delivered to their home, they will receive $50 off if the dryer has any dents or scratches. A randomly selected drier may or may not have any dents or scratches. The hypotheses can be stated as follows. H 0 : The dryer is not dented or scratched. H a : The dryer is dented or scratched. Which of the following best describes a Type I error? a. concluding the dryer is not dented or scratched when it really is b. concluding the dryer is not dented or scratched when it really is not c. concluding the dryer is dented or scratched when it really is d. concluding the dryer is dented or scratched when it really is not e. It is not possible to make a Type I error in this situation. ____ 9. A manager wants to determine the proportion p of employees that arrive to work late. She will call a company meeting if there is clear evidence that this proportion is greater than 0.10 She selects a random sample of 30 employees from the 500 employees at this company to test the hypotheses H 0 :  p  = 0.10, H a :  p  > 0.10. Which condition for inference has not been met in this situation, if any? a. The data are a random sample from the population of interest. b. The sample size is less than 10% of the population size. c. np ³ 10 and n (1 – p ³ 10 d. None of the conditions are violated. e. More than one condition is violated. ____ 10. A buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten. She will only accept the shipment if there is clear evidence that this proportion is less than 0.06 She selects a random sample of 200 apples from the over 20,000 apples on the truck to test the hypotheses H 0 : p = 0.06, H a : p < 0.06. The sample contains 9 rotten apples. Which of the following intervals contains the P -value for this test?

c. d. e. ____ 14. In 2016, 2.6% of all vehicles registered in California were motorcycles. In a random sample of 300 vehicles entering Yosemite National Park that year, 12 of them were motorcycles. We would like to know if this provides sufficient evidence (using  = 0.05) that the proportion of motorcycles entering the park is higher than the proportion that are registered in California. Which of the following is the correct conclusion for the appropriate test of significance? a. Yes, because the P- value = 0.0638 >  = 0.05 we reject H 0 and conclude that the true proportion of motorcycles entering the park is higher than the proportion registered in California. b. No, because the P- value = 0.0638 >  = 0.05 we fail to reject H 0 and cannot conclude that the true proportion of motorcycles entering the park is higher than the proportion registered in California. c. Yes, because the P- value = 0.1075 >  = 0.05 we reject H 0 and conclude that the true proportion of motorcycles entering the park is higher than the proportion registered in California. d. No, because the P- value = 0.1075 >  = 0.05 we fail to reject H 0 and cannot conclude that the true proportion of motorcycles entering the park is higher than the proportion registered in California. e. We cannot perform this test because the conditions for inference have not been met. ____ 15. Suppose you are conducting a test of significance for which H 0 : p = 0.45. Which of the following tests against a specific alternative hypothesis has the greatest power? a. H a : p = 0.48, with n = 40 and  = 0.05 b. H a : p = 0.48, with n = 50 and  = 0.05 c. H a : p = 0.51, with n = 50 and  = 0.05 d. H a : p = 0.51, with n = 40 and  = 0.01 e. H a : p = 0.51, with n = 50 and  = 0.01 ____ 16. Are women more likely to exercise than men? A random sample of 250 women found that 59.2% exercise at least 3 times per week and a random sample of 250 men found that 50% exercise at least 3 times per week. Let p 1 = the proportion of all women that exercise at least 3 times per week, and p 2 = proportion of all men that exercise at least 3 times per week. We would like to know if this is convincing evidence that a greater proportion of women than men exercise at least 3 times per week. What is the value of , the combined (pooled) proportion of successes? a. 273/500 b. 109.2/500 c. 125/250 d. 148/250 e. 136.5/500 ____ 17. An SRS of 45 male employees at a large company found that 36 felt that the company was supportive of female employees. An independent SRS of 40 female employees found that 24 felt that the company was supportive of female employees. Let p 1 = the proportion of all male employees at the company who hold this opinion and p 2 = the proportion of all female employees at the company who hold this opinion. We want to test the hypotheses H 0  :  p 1  –  p 2  = 0; H a  :  p 1  –  p 2     0. Which of the following is the correct test statistic?

a. b. c. d. e. ____ 18. A sociologist hypothesizes that couples who have a child within the first three years of marriage are more likely to divorce. From city records, she selects a random sample of 400 couples in which both the husband and wife were between the ages of 20 and 25 when they married. She compared the divorce rate of couples who had a child within the first three years of marriage to the divorce rate of couples who did not. Here are the results: Child within three years? Yes No Total Divorced within five years? Yes 83 52 135 No 137 128 265 Total 220 180 400 Let p 1 = proportion of all couples that had a child within the first three years and were divorced within five years and p 2 = proportion of all couples that did not have a child within the first three years and were divorced within five years. We wish to test the hypotheses H 0  :  p 1  –  p 2     0, H a  :  p 1  –  p 2     0. Which of the following is the correct test statistic? a. b. c.

who feel that the company is supportive of female employees is higher than the proportion of women who feel this way. d. Accept H a . We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way. e. Fail to reject H 0 . We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way. ____ 22. Sixty-eight people from a random sample of 128 residents of Uppsala, Sweden, had blue eyes. Forty-five people from a random sample of 110 people from Preston, England, had blue eyes. Let p 1 = the proportion of people in Uppsala with blue eyes, and let p 2 = the proportion of people in Preston with blue eyes. We want to test the hypotheses H 0  :  p 1  –  p 2     0, H a  :  p 1  –  p 2   ¹  0 using   = 0.05. The P -value for this test is 0.06. If the researchers use  = 0.05, which of the following represents the correct conclusion to draw from this result? a. Reject H 0 . There is evidence to suggest a difference in the proportion of blue-eyed people in these two countries. b. Fail to reject H 0 . There is convincing evidence to suggest that there is a difference in the proportion of blue-eyed people in these two countries. c. Fail to reject H 0 . There is not convincing evidence to suggest that there is a difference in the proportion of blue-eyed people in these two countries. d. Accept H a . There is convincing evidence to suggest that there is a difference in the proportion of blue-eyed people in these two countries. e. Accept H 0 . There is not convincing evidence to suggest that there is a difference in the proportion of blue-eyed people in these two countries.