The following samples are observations taken from the same elements at two different times: Perform a test of hypothesis to determine if the difference in the means of the distribution at the first time period is 10 units larger than at the second time period.Use a level of significance equal to 0.10. A)Because t = 1.98 2.0150,the null hypothesis must be rejected. B)Because t = 1.67 2.0150,the null hypothesis must be rejected C)Because t = 1.02

Question

The following samples are observations taken from the same elements at two different times: Perform a test of hypothesis to determine if the difference in the means of the distribution at the first time period is 10 units larger than at the second time period.Use a level of significance equal to 0.10. A)Because t = 1.98 > 2.0150,the null hypothesis must be rejected. B)Because t = 1.67 > 2.0150,the null hypothesis must be rejected C)Because t = 1.02 < 2.0150,the null hypothesis cannot be rejected. D)Because t = 0.37 < 2.0150,the null hypothesis cannot be rejected.

Quizplus · Accepted Answer

To test the hypothesis, we need to use a two-sample t-test. Assuming equal variances and using a significance level of 0.10, we find a t-value of 0.37. 
Since 0.37 is less than the critical value of 2.0150, we cannot reject the null hypothesis that the difference in means is not 10 units larger at the first time period compared to the second time period. Therefore, choice D is the best answer.

The Following Samples Are Observations Taken from the Same Elements