New York Survey Data

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.
Determine the point estimate, and then construct the 95% confidence interval for μ7= the average attitude
toward Springdale Mall.
Repeat part (a) for μ8 and μ9, the average attitudes toward Downtown and West Mall, respectively.
Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate, and
construct the 95% confidence interval for p26= the population proportion of males.
Given the breakdown of responses for variable 28 (marital status of respondent), determine the point estimate,
and then construct the 95% confidence interval for p28 = the population proportion in the “single or other”
category.
Assume the managers have requested estimates of the mean attitudes towards each mall with a margin of
error of 0.05 for each mall. If the managers want to have 95% confidence that the sample mean will fall within
this margin of error, how large should the sample size be for each mall?