Stephanie believes that the average running time of movies is equal to 140 minut

Question

Stephanie believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the distribution of the population is normally distributed. 150 150 180 170 State the null and alternative hypotheses. Using a critical value, test the hypothesis at the 10% level of significance. Using a p- value, test the hypothesis at the 10% level of significance. Using a confidence interval, test the hypothesis at the 10% level of significance. Could a Type II error have been committed in this hypothesis test?

Explanation / Answer

a) H0:mu=140 (average run time for movies is equal to 140 minutes)

b) Compute 1-sample t test (for small sample size and knwon standard devation)

t=(xbar-mu)/(s/sqrt n), where xbar is sample mean, and mu is population mean, n i ssample size.

=(162.50-140)/(15/sqrt 4)

=3

b)

The critical t value at df=3, and alph=0.10 is 2.353. The test statistic falls in critical region. Therefore, reject H0, to conclude that avergae running time of movies is different from 140 minutes.

c)

p value is 0.0576. The p value is less than alpha=0.10, reject H0, to cocnclude that avergae running time of movies is different from 140 minutes.

d) The 95% C.I=xbar+-t3,0.10*SE(xbar)

=162.50+-2.353*(15/sqrt4)

=144.8525 to 180.1475.

The interval does not contain 0, therefore, result is significant at alpha=0.10.

e) A Type II error (failure to reject false H0) is not possible.

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