D582 Introduction statistics for Research (ASO1)

40. A researcher measured the reported distances of two small groups of randomly selected GPS units. They found that the difference in sample means (M1 – M2) is 0.22 miles.
Which conclusion is appropriate from a t-test of the hypothesis H0: M1 = M2 versus Ha: M1 ≠ M2 if the p-value is 0.025 and the significance level is α = 0.05?

A. Fail to reject H0 because there is insufficient evidence that the mean reported distance difference is not 0 miles.

B. Reject H0 based on evidence that the mean reported distance difference is not 0 miles.

C. Reject Ha based on evidence that the mean reported distance difference is equal to 0 miles.

D. Fail to reject Ha based on the fact that the mean difference of 0.22 miles is greater than 0 miles.

41. In a study, the GPAs of two small groups of randomly selected students are measured. The difference in sample means (M1 – M2) is -0.12. A t-test of the hypothesis H0: M1 = M2 versus Ha: M1 ≠ M2 is set up. The test statistic is -2.0, and the critical values are -2.998 and 2.998.
What is the appropriate conclusion?

A. Fail to reject Ha based on the fact that the mean difference of -0.12 is less than 0.

B. Reject H0 based on evidence that the mean GPA difference is not 0.

C. Fail to reject H0 because there is insufficient evidence that the mean GPA difference is not 0.

D. Reject Ha based on evidence that the mean GPA difference is equal to 0.

42. In a study, the reported distances of two small groups of randomly selected GPS units are measured. The difference in sample means (M1 – M2) is -0.12 miles. A t-test of the hypothesis H0: M1 = M2 versus Ha: M1 ≠ M2 is set up. The test statistic is -2.84, and the critical values are -2.228 and 2.228.
What is the appropriate conclusion?

A. Reject Ha based on evidence that the mean reported distance difference is equal to 0 miles.

B. Reject H0 based on evidence that the mean reported distance difference is not 0 miles.

C. Fail to reject Ha based on the fact that the mean difference of -0.12 miles is less than 0 miles.

D. Fail to reject H0 because there is insufficient evidence that the mean reported distance difference is not 0 miles.

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