Question

It is desired to compare the average test scores at the two schools. Suppose that random samples of college freshmen are selected from two universities: 15 students from school A and 17 students from school B. The summary statistics of a standardized test are given in the following table. Test if there is a difference in mean test scores at the two schools, assuming that test scores came from normal distributions. Use a 0.05 level of significance. Sample Size | Average Score | Standard Deviation ------------|---------------|------------------ School A (1) | 15 | 100 | 15 School B (2) | 17 | 90 | 18 Part A: What hypothesis test should be used? a. Independent samples t-test b. Matched pairs t-test c. Independent samples z-test d. Test for two proportions Part B: What are the null and alternative hypotheses? a. H0: mu1-mu2=0, Ha: mu1-mu2 <0 b. H0: mu1-mu2 not=0, Ha: mu1-mu2=0 c. H0: mu1-mu2=0, Ha: mu1-mu2 not=0 d. H0: mu1-mu2=0, Ha: mu1-mu2 >0 Part C: Compute the value of the pooled variance. a. 277.8 b. 15.6 c. 16.6 d. 260.4 Part D: Find the value of the test statistic. a. -1.694 b. -0.287 c. 1.694 d. 0.287 Part E: Find the rejection region. a. z<-1.960 and z>1.960 b. t<-1.697 and t>1.697 c. t>1.697 d. t<-2.042 and t>2.042 Part F: What is your decision? a. Do not reject H0, because the value of the test statistic falls in the rejection region. b. Do not reject H0, because the value of the test statistic does not fall in the rejection region. c. Reject H0, because the value of the test statistic does not fall in the rejection region. d. Reject H0, because the value of the test statistic falls in the rejection region. Part G: Interpret the conclusion in the context of the problem. At the 0.05 level of significance, a. There is not sufficient evidence of a difference in mean test scores between the two schools. b. There is not sufficient evidence that the mean test scores are equal. c. There is sufficient evidence that the mean test scores are equal. d. There is sufficient evidence of a difference in mean test scores between the two schools.

It is desired to compare the average test scores at the two schools. Suppose that random samples of college freshmen are selected from two universities: 15 students from school A and 17 students from school B. The summary statistics of a standardized test are given in the following table. Test if there is a difference in mean test scores at the two schools, assuming that test scores came from normal distributions. Use a 0.05 level of significance.

Sample Size | Average Score | Standard Deviation
------------|---------------|------------------
School A (1) | 15 | 100 | 15
School B (2) | 17 | 90 | 18

Part A: What hypothesis test should be used?
a. Independent samples t-test
b. Matched pairs t-test
c. Independent samples z-test
d. Test for two proportions

Part B: What are the null and alternative hypotheses?
a. H0: mu1-mu2=0, Ha: mu1-mu2 <0
b. H0: mu1-mu2 not=0, Ha: mu1-mu2=0
c. H0: mu1-mu2=0, Ha: mu1-mu2 not=0
d. H0: mu1-mu2=0, Ha: mu1-mu2 >0

Part C: Compute the value of the pooled variance.
a. 277.8
b. 15.6
c. 16.6
d. 260.4

Part D: Find the value of the test statistic.
a. -1.694
b. -0.287
c. 1.694
d. 0.287

Part E: Find the rejection region.
a. z<-1.960 and z>1.960
b. t<-1.697 and t>1.697
c. t>1.697
d. t<-2.042 and t>2.042

Part F: What is your decision?
a. Do not reject H0, because the value of the test statistic falls in the rejection region.
b. Do not reject H0, because the value of the test statistic does not fall in the rejection region.
c. Reject H0, because the value of the test statistic does not fall in the rejection region.
d. Reject H0, because the value of the test statistic falls in the rejection region.

Part G: Interpret the conclusion in the context of the problem. At the 0.05 level of significance,
a. There is not sufficient evidence of a difference in mean test scores between the two schools.
b. There is not sufficient evidence that the mean test scores are equal.
c. There is sufficient evidence that the mean test scores are equal.
d. There is sufficient evidence of a difference in mean test scores between the two schools.

Added by Austin C.

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