# statistic homework

**Springdale Shopping Survey **(70 Points)

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 section, hypothesis testing will be used to examine the significance of some of the survey results. From a managerial perspective, the information gained from this database exercise would be useful in determining whether the mean attitude toward a given area differed significantly from the “neutral” level, in observing and comparing the mean attitude scores exhibited toward the three shopping areas, and in examining the strengths and weaknesses of a manager’s shopping area relative to the other two areas. If such a study were repeated from time to time, management could observe the extent to which the overall attitude toward their shopping area was becoming stronger or weaker in the eyes of the consumer, thus helping them select business strategies that could retain and take advantage of their area’s strengths and either correct or minimize the effect of its weaknesses.

- 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.
- Calculate the mean attitude score toward the Springdale Mall shopping area and compute the sample standard deviation. Does this area seem to be well regarded by the respondents?
- In a two-tail test at the 0.10 level, compare the sample mean calculated in part (a) to the 3.0 “neutral” value. Use the null hypothesis H
_{0}: u = 3.0 and the alternative hypothesis H_{1}: u ≠ 3.0. - Generate the 90% confidence interval for the population mean and use this interval in verifying the conclusion obtained in part (b).
- What is the p-value associated with the hypothesis test?
- Repeat parts (a) through (d) for the Downtown shopping area.
- Repeat parts (a) through (d) for the West Mall shopping area.

- If Springdale Mall offered exactly the same benefits as the other two shopping areas, we would expect exactly one-third of those who expressed an opinion to select it as the area best fitting the description for variable number 10 (“Easy to return/exchange goods”). In testing whether Springdale Mall differs significantly from this expected proportion, the null and alternative hypotheses will be H
_{0}: π = 0.333 and H_{1}: π ≠ 0.333. Carry out the following analyses for Springdale Mall:- Analyzing the data for variable 10, use the preceding null and alternative hypotheses in testing the null hypothesis at the 0.05 level.
- Determine the p-value for the test conducted in part (a).
- Repeat parts (a) and (b) for variables 11–17.
- Based on the preceding analyses, identify the principal strengths and weaknesses exhibited by Springdale Mall.

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