Question

Nancy believes that the average running time of movies is equal to 170 minutes. A sample of 7 movies was

taken and the following running times were obtained. Assume the population of the running times is normally

distributed as 158 162, 170 182,185,189,195 Using the p-value approach as well as critical value approach, test

the hypotheses at the 10% level of significance.

Answer 1

Let denote the population mean of movies running time. Then the null and alternative hypothesis here is:

To test this hypothesis we should be using one sample T-test as the population of the running times is given to be normally distributed and the population standard deviation is not given. Thus, the test statistic is

AThe above test statistic follows at distribution with n-1= 6 degrees of freedom. Thus critical value at level;l =0.1 is 1.943. Also, the p-value is

Thus using both the critical value and p-value approach, we can conclude that movie running time is not significantly different from 170.