A student believes that the average grade on the statistics final examination was 87. A sample of 36 past final examinations was taken. The average grade in the sample was 83.96 with a standard deviation of 12. (full calculation)

1. State the null and alternative hypotheses. My Answer: Ho: = 87, Ha: 87
2. Using the critical value approach, test the hypotheses at the 5% level of significance. My partial Answer: = 0.05, /2 = 0.025

z 0.025 = 1.96, t = (83.96 - 87) / (12 / 36) = -1.52, Since -1.52 -1.96 or 1.96, we accept Ho. (we cannot reject Ho)

3. Using the p-value approach, test the hypotheses at the 5% level of significance.

*I ask for the correct answer and full calculation for each question.