The case in Chapter 2 listed 30 questions asked of 150 respondents in the community of Springdale. The coding key for the responses was also provided in that earlier exercise. The data are in file SHOPPING. In this exercise, some of the estimation techniques presented in the chapter will be applied to the survey results. You may assume that these respondents represent a simple random sample of all potential respondents within the community and that the population is large enough that application of the finite population correction would not make an appreciable difference in the results.
1. Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent’s general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement.
a. Determine the point estimate, then construct the 95% confidence interval for π7 = the average attitude toward Springdale Mall. What is the maximum likely error in the point estimate of the population mean?
b. Repeat part (a) for μ8 and μ9, the average attitudes toward Down town and West Mall, respectively.
2. Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate, then construct the 95% confidence interval for π26 = the population proportion of males. What is the maximum likely error in the point estimate of the population proportion?
3. Given the breakdown of responses for variable 28 (marital status of respondent), determine the point estimate, then construct the 95% confidence interval for π28 = the population proportion in the “single or other” category. What is the maximum likely error in the point estimate of the population proportion?