Question

A movie critic claims the mean run time for movies in theaters is 100 minutes. Researchers are trying to prove that the mean run time is actually longer than that though (Ha : µ > 100). In a random sample of 16 movies, the mean run time was found to be 105 minutes with a sample standard deviation of 12 minutes. Assume the population is normally distributed. At α = 0.05, is there enough evidence to reject the movie critic’s claim?

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   = 100

Ha : > 100

Test statistic (t) =

= ( - ) / s / n

= (105 - 100) / 12 / 16

Test statistic = 1.67

P-value = 0.0478

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to support the claim.