Nancy believes that the average running time of movies is equal to 140 minutes. A sample of four movies was taken, and the following running times were obtained. Assume the distribution of the population is normally distributed. 150 150 180 170
a. State the null and alternative hypotheses.
b. Using a critical value, test the hypothesis at the 10% level of significance.
c. Using a p-value, test the hypothesis at the 10% level of significance.
d. Using a confidence interval, test the hypothesis at the 10% level of significance.
e. Could a Type II error have been committed in this hypothesis test?
a. H0: ? = 140
Ha: ? ? 140
b. Reject H0, 3 > 2.353 . There is sufficient evidence at ? = .10 to conclude that the average running time of movies differs from 140 minutes.
c. The p-value is approximately equal to .06 . Reject H0; .06 < 0.1 (same conclusion as part b)
d. 144.85 to 180.15; reject H0 (same conclusion as part b)
e. A Type II error could not have been committed since H0 was rejected.
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