The International Council of Shopping Centers reports that the average teenager spends $39 during a shopping trip to the mall. The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and “teenage group. He believes teen shoppers at his mall respond to his promotional efforts by shopping there more often and spending more when they do. Mall management decides to evaluate the promotions director’s success by surveying a simple random sample of 45 local teens and finding out how much they spent on their most recent shopping visit to the mall. The results are listed in data file XR10056. Use a suitable hypothesis test in examining whether the mean mall shopping expenditure for teens in this area might be higher than for U.S. teens as a whole. Indentify and interpret the p-value for the test. Using the 0.025 level of significance, what conclusion do you reach?
For a Z score, find the difference between means divided by the standard error of the means.
H0: mean 1 = mean 2
H1: mean 1 < mean 2
If p > .025, accept null hypothesis (H0). If p < .025, accept H1.
You should have adequate data to do this.
I hope this helps. Thanks for asking.
You should divide by the standard error for the difference between means. Sorry.
To test whether the mean mall shopping expenditure for teens in this area might be higher than for U.S. teens as a whole, we can use a one-sample t-test. The null hypothesis would be that there is no difference in mean expenditure between local teens and U.S. teens as a whole, while the alternative hypothesis would be that the mean expenditure for local teens is higher.
Here are the steps to perform the hypothesis test:
Step 1: Formulate the hypotheses:
- Null hypothesis (H0): The mean mall shopping expenditure for local teens is the same as the mean expenditure for U.S. teens as a whole.
- Alternative hypothesis (Ha): The mean mall shopping expenditure for local teens is higher than the mean expenditure for U.S. teens as a whole.
Step 2: Set the significance level (alpha):
In this case, using the 0.025 level of significance means that we want to be 95% confident in our conclusion.
Step 3: Conduct the test:
We will use the given data file (XR10056) which contains the shopping expenditures of a random sample of 45 local teens. We will calculate the mean and standard deviation of this sample and compare it to the population mean of U.S. teens' shopping expenditure.
Step 4: Calculate the test statistic and p-value:
Using the sample mean, sample standard deviation, population mean, and sample size, we can calculate the t-test statistic. From this test statistic, we can then calculate the p-value.
Step 5: Make a decision:
If the p-value is less than the significance level (alpha), we reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.
Now, we need the actual data file (XR10056) to calculate the test statistic and p-value. Once we have that, we can continue with the hypothesis test and determine the conclusion.