Commute Times: According to the New York Times Almanac, a survey of 15 large U.S. cities found that the average commute time one way to work was 25.4 minutes. A chamber of commerce executive feels that the one way to work commute in her city is less than this and wants to publicize this. In order to assess her belief, she randomly selected 25 commuters in her city and found the average one way commute time to work to be 22.1 minutes with a standard deviation of 5.3 minutes. At a 1% significance level assess the validity of the claim she would like to advertise for her city. a. What is the inherent question of interest here? b. What might be a reasonable description of the population of interest? c. What is the relevant sample here? d. What is the random variable being evaluated here? e. What is the population parameter of interest? f. What is this parameter’s corresponding sample statistic? g. What is an appropriate research hypothesis to consider? h. What is the corresponding null hypothesis? i. What is the test statistic used to test these hypotheses? j. What is the null distribution of this test statistic? k. What is the decision rule that might be used here (use α = 0.01)? l. What decision was made with regard to the null hypothesis? m. What is your conclusion based on the available data? n. What is your best point estimate of the average one-way commute time to work in this city? o. Provide a 99% confidence interval for the average one-way commute time to work in this city. p. Given the results of your evaluation, do you believe this executive can reasonably make the claim of shorter average commute times for her city than other large U.S. cities? Why or why not?
- Commute Times: According to the New York Times Almanac, a survey of 15 large U.S. cities found that the average commute time one way to work was 25.4 minutes. A chamber of commerce executive feels that the one way to work commute in her city is less than this and wants to publicize this. In order to assess her belief, she randomly selected 25 commuters in her city and found the average one way commute time to work to be 22.1 minutes with a standard deviation of 5.3 minutes. At a 1% significance level assess the validity of the claim she would like to advertise for her city.
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a. What is the inherent question of interest here? |
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b. What might be a reasonable description of the population of interest? |
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c. What is the relevant sample here? |
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d. What is the random variable being evaluated here? |
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e. What is the population parameter of interest? |
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f. What is this parameter’s corresponding sample statistic? |
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g. What is an appropriate research hypothesis to consider? |
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h. What is the corresponding null hypothesis? |
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i. What is the test statistic used to test these hypotheses? |
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j. What is the null distribution of this test statistic? |
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k. What is the decision rule that might be used here (use α = 0.01)? |
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l. What decision was made with regard to the null hypothesis? |
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m. What is your conclusion based on the available data? |
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n. What is your best point estimate of the average one-way commute time to work in this city? |
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o. Provide a 99% confidence interval for the average one-way commute time to work in this city. |
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p. Given the results of your evaluation, do you believe this executive can reasonably make the claim of shorter average commute times for her city than other large U.S. cities? Why or why not? |
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