1. In a recent utilization survey of an e-learning platform of a post-secondary institution, a random sample of 64 students is selected (out a of a population of 5000 students). Their weekly hours of using this platform to perform learning activities are collected.After analyzing the data, a researcher states that he is 95% confident that the mean hours of the 5000 students is between 36.2 and 40.8 hours.

a. Explain the meaning of the statement reported by the researcher.

b. Suppose the population mean hours is later found to be 35.4 hours. The confidence interval reported by the researcher failed to cover the population mean. Discuss if there is anything wrong with the interval?

2. The property manager of a shopping mall claims that the mean score of their customer service is at least 85.Twenty-five customers were randomly selected to evaluate the customer service of the mall. The analysis via a hypothesis test shows that the P-value is less than 0.002 (i.e. p < 0.002).

a. State the null and alternative hypotheses.

b. Which distribution, normal or Student's t-distribution, is more appropriate for the hypothesis test? Why?

c. Explain the results of the hypothesis test in a way that could be understood by someone who has not studied statistics.

3. One study shows 60% of CEOs in the U.S hold a master's degree or doctorate. 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?

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.

7. In a completely randomized design, 7 experimental units were used for each of the three levels of the factor.

Source of Variation Sum of Squares Degrees of Freedom Mean Square F

Treatment

Error 432076.5

Total 675643.3

a. Complete the ANOVA table.

b. Find the critical value at the 0.05 level of significance from the F-table for testing whether the population means for the three levels of the factors are different.

c. Use the critical value approach and = 0.05 to test whether the population means for the three levels of the factors are the same.

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