Gnap (1995) conducted a survey to estimate the teacher workload in Maricopa County, Arizona, public school districts. Her target population was all first through sixth grade full-time public school teachers with at least one year of experience. In 1994, Maricopa County had 46 school districts with 311 elementary schools and 15,086 teachers. Gnap stratified the schools by size of school district; the large stratum, consisting of schools in districts with more than 5000 students, is considered in this exercise. The stratum contained 245 schools; 23 participated in the survey. All teachers in the selected schools were asked to fill out the questionnaire. Due to non response, however, some questionnaires were not returned. (We shall examine possible effects of non response in Exercise 12 of Chapter 8.) The data are in file teachers.dat, with psu information in teachmi.dat.
a. Why would a cluster sample be a better design than an SRS for this study? Consider issues such as cost, ease of collecting data, and confidentiality of respondent. What are some disadvantages of using a cluster sample?
b. Calculate the mean and standard deviation of hrwork for each school in the “large” stratum. Construct a graph of the means for each school and a separate graph of the standard deviations. Does there seem to be more variation within a school, or does more of the variability occur between different schools? How did you deal with missing values (coded as −9)?
c. Construct a scatterplot of the standard deviations versus the means for the schools, for the variable hrwork. Is there more variability in schools with higher workloads? Less? No apparent relation?
d. Estimate the average of hrwork in the large stratum in Maricopa County, along with its standard error. Use popteach in teachmi.dat for the Mi’s.