4. 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.

6. The Ministry of health in BC wants to compare the average amount of time people spend in the Stanly Park versus English Bay during peak times to implement effective safety measures for COVID-19. A random sample of 25 persons in the Stanly Park spent an average of 14.6 minutes with a sample standard deviation of 5.8 minutes. A random sample of 27 persons in the English Bay spent an average of 11.5 minutes with a sample standard deviation of 4.9 minutes.

Perform a hypothesis test using = 0.05 to determine if the average time people spend in the Stanly park is more than the average time people spend in the English Bay.