A student believes that the average grade on the statistics final examination was 86. A sample of 36 past final examinations was taken. The average grade in the sample was84.91with a standard deviation of 12.

(a)

State the null and alternative hypotheses. (Enter != foras needed.)

H₀:

H_a:

(b)

Using the critical value approach, test the hypotheses at the 5% level of significance.

Compute the test statistic.

Determine the critical value(s) for this test. (Round your answer(s) to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistictest statistic

State your conclusion.

RejectH₀. There is sufficient evidence to conclude that the average grade on the statistics final examination differs significantly from 86.

Do not rejectH₀. There is sufficient evidence to conclude that the average grade on the statistics final examination differs significantly from 86.

RejectH₀. There is insufficient evidence to conclude that the average grade on the statistics final examination differs significantly from 86.

Do not rejectH₀. There is insufficient evidence to conclude that the average grade on the statistics final examination differs significantly from 86.

(c)

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

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

RejectH₀. There is sufficient evidence to conclude that the average grade on the statistics final examination differs significantly from 86.

Do not rejectH₀. There is sufficient evidence to conclude that the average grade on the statistics final examination differs significantly from 86.

RejectH₀. There is insufficient evidence to conclude that the average grade on the statistics final examination differs significantly from 86.

Do not rejectH₀. There is insufficient evidence to conclude that the average grade on the statistics final examination differs significantly from 86.