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In January 1995, the Office of University Evaluation at Arizona State University surveyed faculty and staff members to find out their reaction to the closure of the university during Winter Break, 1994. Faculty and staff in academic units that were closed during the winter break were divided into four strata and subsampled.

Questionnaires were sent through campus mail to persons in strata 1 through 4; the sample size in the above table is the number of questionnaires mailed in each stratum. Weâ€™ll come back to the issue of nonresponse in this survey in Chapter 8; for now, just analyze the respondents in the stratified sample of employees in closed units; the data are in the file â€œwinter.dat.â€ For this exercise, look at the answers to the question â€œWould you want to have Winter Break Closure again?â€ (variable breakaga).

a Not all persons in the survey responded to the question. Find the number of persons that responded to the question in each of the four strata. For this exercise, use these values as the nh.

b Use (3.6) and (3.7) to estimate the proportion of faculty and staff that would answer yes to the question â€œWould you want to have Winter Break Closure againâ€ and give the standard error.

c Create a new variable, in which persons who respond â€œyesâ€ to the question take on the value 1, persons who respond â€œnoâ€ to the question take on the value 0, and persons who do not respond are either left blank (if you are using a spreadsheet) or assigned the missing value code (if you are using statistical software). Construct a column of sampling weights Nh/nh for the observations in the sample. (The sampling weight will be 0 or missing for nonrespondents.) Now use (3.10) to estimate the proportion of faculty and staff that would answer yes to the question â€œWould you want to have Winter Break Closure again?â€

d Using the column of 0s and 1s you constructed in the previous question, find s2 h for each stratum by calculating the sample variance of the observations in that stratum. Now use (3.5) to calculate the standard error of your estimate of the proportion. Why is your answer the same as you calculated in (b)?

e Stratification is sometimes used as a method of dealing with nonresponse. Calculate the response rates (the number of persons who responded divided by the number of questionnaires mailed) for each stratum. Which stratum has the lowest response rate for this question? How does stratification treat the nonrespondents?

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