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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. 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?

The mean attitude score toward the Springdale Mall is 3.6467.

This mean value puts the attitude toward Springdale Mall just over midway between “Neutral” and “Like”, so it would be a stretch to consider this mall to be “well regarded”. The rating is actually somewhat better than “indifferent”. 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 and the alternative hypothesis .

The hypotheses are:

Null:

Alternative:

The critical values for a two-tailed test at α = 0.10 are ±1.645.

The test statistic is 6.5436.

Since the test statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

There is sufficient evidence at the 0.10 level of significance to support a claim that the population mean attitude toward Springdale Mall is different from 3.0.

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

The 90% confidence interval for the population mean is (3.4841, 3.8092).

Since the 90% confidence interval does not include the value 3.0, a claim that the population mean attitude toward Springdale Mall is different than 3.0 is

supported.

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

The p-value is 0.0000. e. Repeat parts (a) through (d) for the Downtown shopping area.

The mean attitude score toward the Downtown shopping area is 3.3933.

This mean value puts the attitude toward Downtown shopping area just over the “Neutral” level. While the attitude is positive, it is not necessarily sufficiently different from the “neutral” level to be considered “well regarded”.

The hypotheses are:

Null:

Alternative:

The critical values for a two-tailed test at α = 0.10 are ±1.645.

The test statistic is 4.3612.

Since the test statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

There is sufficient evidence at the 0.10 level of significance to support a claim that the population mean attitude toward the Downtown shopping area is different

from 3.0.

The 90% confidence interval for the population mean is (3.2450, 3.5417).

Since the 90% confidence interval does not include the value 3.0, a claim that the population mean attitude toward the Downtown shopping area is different than

3.0 is supported.

The p-value is 0.0000. f. Repeat parts (a) through (d) for the West Mall shopping area.

The mean attitude score toward the West Mall shopping area is 3.2333.

This mean value puts the attitude toward West Mall shopping area just over the “Neutral” level. While the attitude is positive, it is not necessarily sufficiently different from the “neutral” level to be considered “well regarded”.

The hypotheses are:

Null:

Alternative:

The critical values for a two-tailed test at α = 0.10 are ±1.645.

The test statistic is 2.4373.

Since the test statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

There is sufficient evidence at the 0.10 level of significance to support a claim that the population mean attitude toward the West Mall shopping area is different

from 3.0.

The 90% confidence interval for the population mean is (3.0759, 3.3908).

Since the 90% confidence interval does not include the value 3.0, a claim that the population mean attitude toward the West Mall shopping area is different than

3.0 is supported.

The p-value is 0.0148.

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 . 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.

After removing all of the “4” responses (“4” = “No Opinion”), there are a total of 117 responses, and 60 that indicate a preference for Springdale Mall.

The sample proportion is:

The hypotheses are:

Null:

Alternative:

The critical values for a two-tailed test with α = 0.05 are ±1.96.

The test statistic is:

Since the test statistic is greater than the positive critical value, the decision is to

reject the null hypothesis.

There is sufficient evidence at the 0.05 level of significance to support a claim that the proportion who prefer the Springdale Mall differs from 0.33.

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

The p-value for this test is 0.0000.

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

For the remaining variables, the hypotheses and critical values remain the same.

The tests and the corresponding results are:

Variable 11 (High quality of goods):

Test statistic value: 6.3056