Question: . A statistician argues when sample size is big enough, the probability that the mean of the sample be higher than the mean of the

. A statistician argues when sample size is big enough, the probability that the mean of the sample be higher than the mean of the population is the same as the probability that the mean of the sample be lower than the mean of population. Do you agree or disagree? Discuss your answer.

5. 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 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.

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