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. We'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 winter.csv. For this exercise, look at the answers to the question "Would you want to have Winter Break Closure again?" (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 n_(h).
(b) Use (3.7) and (3.8) to estimate the proportion of faculty and staff that would answer yes to the question "Would you want to have Winter Break Closure again" and give the standard error.
(c) Create a new variable, in which persons who respond "yes" to the question take on the value 1, persons who respond "no" 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 (N_(h))/(n_(h)) for the observations in the sample. (The sampling weight will be 0 or missing for nonrespondents.) Now use (3.11) to estimate the proportion of faculty and staff that would answer yes to the question "Would you want to have Winter Break Closure again."
File asafellow.csv contains the data described in Example 3.7. There are 18 strata, defined by the cross-classification of variables awardyr and gender.
(a) Calculate the sampling weight for each member of the sample. Is the sample exactly self-weighting?
(b) Estimate the proportion of Fellows who work in academia. In 2020, approximately 48% of the population of ASA members worked in academia. Does your 95% CI include the value 0.48?
(c) Estimate the proportion of Fellows who majored in mathematics as undergraduates, along with its standard error. Use the same method as in Example 3.4 to deal with the missing data.