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 a p-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.
a. H0: ? = 87
Ha: ? ? 87
b. Do not reject H0, –1.96 < –1.52 < 1.96 . There is not sufficient evidence at ? = .05 to conclude that the average statistics final exam grade differs from 87.
c. Do not reject H0, 0.1286 > 0.05 (same conclusion as part b)
d. 80.04 to 87.88; do not reject H0 (same conclusion as part b)
e. .8315
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