Question

A student has completed the solution for a hypothesis test as shown below. However, the solution is riddled with errors. Your task is to identify each error and give an explanation as to why that error is incorrect. You will receive 1 point for identifying the error and 1 point for the explanation. Refer to the video in this module titled "Identifying Errors" for how to write out your explanations. Problem: The average moviegoer sees 8.5 movies a year. A random sample of 35 moviegoers revealed that the average number of movies seen per person was 9.6. The population standard deviation is 3.2 movies. At the 0.05 level of significance, can it be concluded that the true number of movies seen by a moviegoer is greater than 8.5 movies a year? Solution: u = The true mean number of movies seen by a moviegoer in a year Ho: * = 8.5 H: * > 8.5 Conditions: i) States a random sample of 35 moviegoers ii) We must assume that the sample comes from a population that is normally distributed 9.6-8.5 Test statistic: t = = 2.03 p-value: 0.042 Conclusion: Since 0.042 <0.05, we fail to reject H. We have significant evidence to suggest that the true mean number of movies seen each year by a moviegoer is equal to 8.5.

Answer 1

Descriptions of Ho and H1 are wrong. Because we draw in ference on unknown parameter (here it is population mean) so the correct descriptions are Ho: p= 8.5, H1: > 8.5. Since population standard deviation is known so we use z test instead of t test. We use t test when population standard deviation is unknown. (9.6 – 8.5) Test statistic : 2= = 2.03 3.2 35 P(Z > 2.03|Z ~ N(0,1)) = 0.021 Sop-value is also wrong. p-value given in the question is for two tail test. p-value Conclusion is also wrong. Since p-value < 0.05, we reject Ho; because p-value < 0.05 → observed value falls in 0.05 level critical region. Hence we conclude that we have significant evidence to suggest that the true mean number of movies seen each year by a moviegoer is greater than 8.5.