A tennis ball manufacturing company claims that more than 98% of tennis balls produced at their factory would pass quality control. A business person is considering purchasing the company and he hires you to test if there is sufficient evidence to support their claim. Suppose a sample of 3152 tennis balls produced at the factory has been collected, and 3100 of them passed quality control.
A. Identify the population of interest to the business person.
B. State the null and the alternative hypotheses. Define all your notation.
C. Which of the Type I and Type II errors is a more serious mistake to make from the perspective of the business person? Describe what the type of error identified means in the context of the question, and explain why it is more serious to make this type of error.
D. List and check any required assumptions/conditions to conduct the hypothesis test in the context of the question.
E. Compute the test statistic. Please keep at least 6 decimal places in all your intermediate steps. Give your final answers to 3 decimal places.
F. Obtain the P-value. Clearly explain your steps.
G. State your conclusion in the context of the question at the 5% significance level.
H. Obtain the 95% confidence interval for the parameter discussed above.
I. Suppose the business person wanted you to re-estimate the proportion of tennis balls passing quality control so that the estimate would be within 0.005 difference compared to the true proportion with 95% confidence. How large a sample is required?