# Question

The Springdale computer database exercise of Chapter 2 listed 30 shopping-related questions asked of 150 respondents in the community of Springdale. The data are in file SHOPPING. The coding key for these responses was also provided in the Chapter 2 exercise. In this section, hypothesis testing will be used to examine the significance of some of the survey 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. 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?

b. 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 H0: μ = 3.0 and the alternative hypothesis H1: μ ≠ 3.0.

c. Generate the 90% confidence interval for the population mean and use this interval in verifying the conclusion obtained in part (b).

d. What is the p-value associated with the hypothesis test?

e. Repeat parts (a) through (d) for the Down town shopping area.

f. Repeat parts (a) through (d) for the West Mall shopping area.

2. 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 H0: π = 0.333 and H1: π ≠ 0.333. Carry out the following analyses for Springdale Mall:

a. Analyzing the data for variable 10, use the preceding null and alternative hypotheses in testing the null hypothesis at the 0.05 level.

b. Determine the p-value for the test conducted in part (a).

c. Repeat parts (a) and (b) for variables 11–17.

d. Based on the preceding analyses, identify the principal strengths and weaknesses exhibited by Springdale Mall.

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. 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?

b. 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 H0: μ = 3.0 and the alternative hypothesis H1: μ ≠ 3.0.

c. Generate the 90% confidence interval for the population mean and use this interval in verifying the conclusion obtained in part (b).

d. What is the p-value associated with the hypothesis test?

e. Repeat parts (a) through (d) for the Down town shopping area.

f. Repeat parts (a) through (d) for the West Mall shopping area.

2. 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 H0: π = 0.333 and H1: π ≠ 0.333. Carry out the following analyses for Springdale Mall:

a. Analyzing the data for variable 10, use the preceding null and alternative hypotheses in testing the null hypothesis at the 0.05 level.

b. Determine the p-value for the test conducted in part (a).

c. Repeat parts (a) and (b) for variables 11–17.

d. Based on the preceding analyses, identify the principal strengths and weaknesses exhibited by Springdale Mall.

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