A simple random sample of 25 movies is taken from a movie website and the average lengths of them are found to be 150 min. The population standard deviation σ is known to be 10 min.

a. Test the hypothesis that the population mean length is greater than 145 min using the 0.05 level of significance.

b. Test the hypothesis that the population mean of movies length is different from 155 min using the critical value approach and a 0.05 level of significance