The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The variables in the survey can be found in the file CODING.
In this exercise, some of the estimation techniques presented in the module will be applied to the Springfield Shopping 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.
Managers associated with shopping areas like these find it useful to have point estimates regarding variables describing the characteristics and behaviors of their customers. In addition, it is helpful for them to have some idea as to the likely accuracy of these estimates. Therein lies the benefit of the techniques presented in this module and applied here.
- 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 = 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 and , the average attitudes toward Downtown and West Mall, respectively.
- Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate, then construct the 95% confidence interval for = the population proportion of males. What is the maximum likely error in the point estimate of the population proportion?
- Given the breakdown of responses for variable 28 (marital status of respondent), determine the point estimate, then construct the 95% confidence interval for = the population proportion in the “single or other” category. What is the maximum likely error in the point estimate of the population proportion?