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# Springdale Shopping Survey

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Please see attached Excel sheet. Also below is the link to the free book for reference. (I would start there!) The question is on Page #308.

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 µ7 = 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 Downtown 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?

https://brainmass.com/math/numerical-analysis/springdale-shopping-survey-554481

#### Solution Preview

See the attachment.

a. Determine the point estimate, then construct the 95% confidence interval for 7 5 the average
attitude toward Springdale Mall. What is the maximum likely error in the point estimate of the population
mean?

Point estimate

Point estimate of Mean, u7 = 4.086
Point estimate of population standard deviation = 0.776
n = 150
z= z value corresponding to the level of confidence desired
Construction of the 95% confidence interval for population mean
The normal distribution for 95% confidence, z will be +- 1.96
So the 95% confidence interval for u is
mean - 1.96(0.776/sqrt(150)
4.086 - 1.96(0.776/12.24)
4.083 - 1.96 (0.06)
4.083 - 0.117= 3.966 OR 4.083 + 0.117 = 4.2
So the 95% confidence interval for u is between 3.966 and 4.2

The maximum standard error of the sampling distribution of the mean is std/ sqrt(150)
0.776 / 12.24 = 0.063

"b. Repeat part (a) for 8 and 9, the average attitudes toward Down ...

#### Solution Summary

The solution discusses the Springdale Shopping survey.

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## Shopping Survey

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 and the survey variables can be found in the attached files. Please address each of the following:

- Construct three different frequency distributions, one each for variables 7, 8, and 9. How do the three areas compare in terms of residents' general attitudes toward each?
- Do people tend to spend differently at the three areas? Construct and compare frequency distributions for variables 4, 5, and 6.
- To find out more about specific strengths and weaknesses of the areas, set up a frequency distribution for variable 10 (e.g., how many "best-fits" votes did each area get for "easy to return/exchange goods"?). Repeat this for variables 11-17 and interpret the results. Which of the malls seems to be the "bargain mall"? Which area seems to have the most convenient shopping hours?
- To find out more about the shoppers in the areas, set up a frequency distribution table to find out the number of male and female shoppers (Variable 26); the number of years each shopper has for education completed (Variable 27); and the marital status (Variable 28). Then find the average number of people in the house as well as the average age of the shopper interviewed. Interpret the results.

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