1. (25 points) The property manager of a shopping mall claims that the mean score of

their customer service is greater than 85. Twenty-ve customers were randomly selected

to evaluate the customer service of the mall. The average and standard deviation of the

sample was found to be 87 and 7 respectively. Test the hypothesis at = 0:05.

2. (25 points) One study shows 60% of CEOs in the U.S hold a master's degree or doctor-

ate. A random sample of 400 CEOs are selected in U.S. What is the probability that

less than 55% of them have a master's degree or doctorate?

3. (50 points) 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 sample standard deviation is

10 min.

(1) (25 points) Test the hypothesis that the population mean length is greater than

145 min using the 0.05 level of signicance.

(2) (25 points) Test the hypothesis that the population mean of movies length is less

than 155 min using the critical value approach and a 0.05 level of signicance.