Investigators selected an SRS of 200 high school seniors from a population of 2000 for a survey of television-viewing habits, with an overall response rate of 75%. By checking school records, they were able to find the grade point average for the non respondents, and classify the sample accordingly:

a. What is the estimate for the average number of hours of TV watched per week if only respondents are analyzed? What is the standard error of the estimate?
b. Perform a χ2 test for the null hypothesis that the three GPA groups have the same response rates. What do you conclude? What do your results say about the type of missing data: Do you think the data are MCAR? MAR? Non ignorable?
c. Perform a one way ANOVA analysis to test the null hypothesis that the three GPA groups have the same mean level of television viewing. What do you conclude? Does your ANOVA analysis indicate that GPA would be a good variable for constructing weighting cells? Why, or why not?
d. Use the GPA classification to adjust the weights of the respondents in the sample. What is the weighting class estimate of the average viewing time?
e. The population counts are 700 students with GPA between 3 and 4; 800 students with GPA between 2 and 3; and 500 students with GPA less than 2. Use these population counts to construct a post stratified estimate of the mean viewing time.

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Sample Number of Hours of TV RespondentsySy 32 15 19 54 25 GPA Size 3.00-4.00 2.00-2.99 Below 2.00 75 72 53 58 26 41 Total 200 150