A decision-maker wishes to test the null and alternative hypotheses shown to the right using an alpha level equal to 0.01. The population standard deviations are assumed to be known. After the sample...

Extracted text: A decision-maker wishes to test the null and alternative hypotheses shown to the right using an alpha level equal to 0.01. The population standard deviations are assumed to be known. After the sample data are collected, the test statistic is computed to be z = 1.54. Complete parts a through c below. Ho: H1 - H2 =0 HA: H4-H2 #0 a. Using the test statistic approach, what conclusion should be reached about the null hypothesis? Determine the critical value(s) for a = 0.01. Select the correct choice below and fill in the answer box to complete your choice. (Round to two decimal places as needed.) O A. - Za = В. Za = OC. + Za/2 = + State the conclusion. Choose the correct answer below. O A. Do not reject the null hypothesis. There is not sufficient evidence at a = 0.01 to suggest that the difference of the population means is different from 0. O B. Reject the null hypothesis. There is sufficient evidence at a = 0.01 to suggest that the difference of the population means is different from 0. OC. Do not reject the null hypothesis. There is sufficient evidence at a = 0.01 to suggest that the difference of the population means is different from 0. O D. Reject the null hypothesis. There is not sufficient evidence at a = 0.01 to suggest that the difference of the population means is different from 0. b. Using the p-value approach, what decision should be reached about the null hypothesis? Determine the p-value. p-value = (Round to four decimal places as needed.) State the conclusion. Choose the correct answer below. O A. Reject the null hypothesis. There is not sufficient evidence at a = 0.01 to suggest that the difference of the population means is different from 0. B. Do not reject the null hypothesis. There is sufficient evidence at a = 0.01 to suggest that the difference of the population means is different from 0. O C. Reject the null hypothesis. There is sufficient evidence at a = 0.01 to suggest that the difference of the population means is different from 0. O D. Do not reject the null hypothesis. There is not sufficient evidence at a= 0.01 to suggest that the difference of the population means is different from 0. c. Will the two approaches (test statistic and p-value) ever provide different conclusions based on the same sample data? Explain. O A. Yes, because it is possible for a test statistic not in the rejection region determined by the critical value(s) to have a p-value less than a. B. No, because a test statistic in the rejection region determined by the critical value(s) will always have a p-value greater than or equal to a. C. No, because a test statistic in the rejection region determined by the critical value(s) will always have a p-value less than a. D. Yes, because it is possible for a test statistic in the rejection region determined by the critical value(s) to have a p-value greater than or equal to a.