A student believes that the average grade on the statistics final examination is 87. A sample of 36 final examinations is taken. The average grade in the sample is 83.96. The population variance is 144.

a. State the null and alternative hypotheses.

b. Using a critical value, test the hypothesis at the 5% level of significance.

c. Using ap-value, test the hypothesis at the 5% level of significance.

d. Using a confidence interval, test the hypothesis at the 5% level of significance. e. Compute the probability of a Type II error if the average grade on the final is 85.

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