Chapter 10: Two Sample Tests MULTIPLE CHOICE. Choose the …

1 Chapter 10: Two- Sample Tests MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) True or False: For all two- Sample Tests , the Sample sizes must be equal in the two groups. 1). A) True B) False 2) The t test for the di erence between the means of 2 independent populations assumes that the 2). respective A) populations are approximately normal. B) Sample sizes are equal. C) Sample variances are equal. D) All of the above. 3) True or False: When you test for differences between the means of two independent 3). populations, you can only use a two-tail test.

2 A) True B) False SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. SCENARIO 10-4. Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The rst Sample has a mean of and standard deviation of while the second Sample has a mean of and standard deviation of 4) Referring to Scenario 10-4, the pooled ( , combined) variance is _____. 4). 5) Referring to Scenario 10-4, the computed t statistic is _____. 5). 6) Referring to Scenario 10-4, there are _____ degrees of freedom for this test.

3 6). MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) If we are testing for the di erence between the means of 2 independent populations presuming 7). equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to A) 18. B) 19. C) 39. D) 38. 8) In testing for differences between the means of two independent populations, the null 8). hypothesis is A) H0 : 1 - 2 = 2. B) H0 : 1 - 2 < 2. C) H0 : 1 - 2 > 0. D) H0 : 1 - 2 = 0. 1. 9) Given the following information, calculate the degrees of freedom that should be used in the 9).

4 Pooled-variance t test. s1 2 = 4 s2 2 = 6. n1 = 16 n2 = 25. A) df = 41 B) df = 16 C) df = 25 D) df = 39. SCENARIO 10-1. Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample Size 211 100. Sample Mean SSATL Score Sample Std. Dev. 10) Referring to Scenario 10-1, judging from the way the data were coll ected, which test would 10). likely be most appropriate to employ? A) Pooled-variance t test for the difference between two means B) Paired t test C) F test for the ratio of two variances D) Z test for the difference between two proportions 11) Referring to Scenario 10-1, give the null and alternative hypotheses to determine if the mea n 11).

5 SSATL score of Japanese managers differs from the mean SSATL score of American managers. A) H0 : A - J 0 versus H1 : A - J > 0 B) H0 : A - J = 0 versus H1 : A - J 0. C) H0 : X A - X J = 0 versus H1 : X A - X J 0 D) H0 : A - J 0 versus H1 : A - J < 0. 12) Referring to Scenario 10-1, what is the value of the test statistic? 12). A) B) C) D) 13) Referring to Scenario 10-1, nd the p-value if we assume that the alternative hypothesis was a 13). two-tail test. A) Smaller than B) Between and C) Greater than D) Between and 2. SCENARIO 10-3. A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.

6 Assume that the two population variances are equal. A random Sample of 100 families from Gotham and a random Sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: X G = 35 months, SG2 = 900 Metropolis: X M = 50 months, SM2 = 1050. 14) Referring to Scenario 10-3, which of the following represents the relevant hypotheses tested by 14). the real estate company? A) H0 : X G - X M 0 versus H1 : X G - X M < 0. B) H0 : G - M 0 versus H1 : G - M < 0. C) H0 : G - M = 0 versus H1 : G - M 0. D) H0 : G - M 0 versus H1 : G - M > 0. 15) Referring to Scenario 10-3, what is the estimated standard error of the di erence between the 2 15).

7 Sample means? A) B) C) D) 16) Referring to Scenario 10-3, what is a point estimate for the mean of the sampling distribution 16). of the di erence between the 2 Sample means? A) -10 B) -22 C) -15 D) 0. 17) Referring to Scenario 10-3, what is(are) the critical value(s) of the relevant hypothesis test if the 17). level of signi cance is A) t Z = B) t Z = C) t Z = D) t Z = 18) Referring to Scenario 10-3, what is(are) the critical value(s) of the relevant hypothesis test if the 18). level of signi cance is A) t Z = B) t Z = C) t Z = D) t Z = 19) Referring to Scenario 10-3, what is the test statistic for the di erence between Sample means?

8 19). A) B) C) D) 20) Referring to Scenario 10-3, suppose = Which of the following represents the result of the 20). relevant hypothesis test? A) The null hypothesis is not rejected. B) Insufficient information exists on which to make a decision. C) The alternative hypothesis is rejected. D) The null hypothesis is rejected. 3. 21) Referring to Scenario 10-3, suppose = Which of the following represents the result of the 21). relevant hypothesis test? A) Insufficient information exists on which to make a decision. B) The null hypothesis is rejected. C) The null hypothesis is not rejected. D) The alternative hypothesis is rejected.

9 22) Referring to Scenario 10-3, suppose = Which of the following represents the result of the 22). relevant hypothesis test? A) Insufficient information exists on which to make a decision. B) The null hypothesis is not rejected. C) The null hypothesis is rejected. D) The alternative hypothesis is rejected. 23) Referring to Scenario 10-3, suppose = Which of the following represents the correct 23). conclusion? A) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. B) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

10 C) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. D) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. 24) Referring to Scenario 10-3, suppose = Which of the following represents the correct 24). conclusion? A) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. B) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.