Figure 2 shows comparative boxplots of the commute times for a random sample of 500 workers...

 
  

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Figure 2 shows comparative boxplots of the commute times for a random sample of 500 workers in Atlanta and 500 workers in St. Louis. We wish to estimate the difference in mean commute time between Atlanta and St. Louis. City Atlanta St. Louis 0 50 1 Figure 2 100 150 Commute Time 200 a. Discuss and compare the shape, center, and any outliers of boxplots in Figure 2. As well, which city appears to have the longer average commute time? 4 points b. Which of the two cities has the higher commute time? Briefly explain 3 points Use the StatKey output of a bootstrap distribution for the difference in mean commute times between the two cities to answer parts c-h that follow: Bootstrap Dotplot of ₁-₂ 250 Left Tail Two-Tail 200 150 100 50 0 3 Right Tail 0.025 4.996 Atlanta St. Louis 0.950 50 7 7.165 Figure 3 Original Sample 1-3-7.14, n=500, 500 ... 29.11 100 8 Figure 4 150 samples-10000 mean 7.165 sid. error 1.123 0.025 9.371 10 11 c. Describe how to compute one bootstrap statistic from this data given that we are interested in the difference in mean commute time between the two cities. 7 points d. Based on Figure 4 above, identify the ₁ and ₂ values. 2 points e. Use the standard error approach to find a 95% confidence interval for the parameter of interest. 5 points f. Using the percentile approach, find a 95% confidence interval for the parameter of interest. 3 points g. Interpret the 95% confidence interval you have provided as an answer to question 4f. 4 points h. Based on the confidence interval provided in 4f can you conclude with 95% confidence that the mean commute time for workers in the Atlanta area differs from the mean commute time for workers in metropolitan St. Louis? Briefly explain. 4 points Figure 2 shows comparative boxplots of the commute times for a random sample of 500 workers in Atlanta and 500 workers in St. Louis. We wish to estimate the difference in mean commute time between Atlanta and St. Louis. City Atlanta St. Louis 0 50 1 Figure 2 100 150 Commute Time 200 a. Discuss and compare the shape, center, and any outliers of boxplots in Figure 2. As well, which city appears to have the longer average commute time? 4 points b. Which of the two cities has the higher commute time? Briefly explain 3 points Use the StatKey output of a bootstrap distribution for the difference in mean commute times between the two cities to answer parts c-h that follow: Bootstrap Dotplot of ₁-₂ 250 Left Tail Two-Tail 200 150 100 50 0 3 Right Tail 0.025 4.996 Atlanta St. Louis 0.950 50 7 7.165 Figure 3 Original Sample 1-3-7.14, n=500, 500 ... 29.11 100 8 Figure 4 150 samples-10000 mean 7.165 sid. error 1.123 0.025 9.371 10 11 c. Describe how to compute one bootstrap statistic from this data given that we are interested in the difference in mean commute time between the two cities. 7 points d. Based on Figure 4 above, identify the ₁ and ₂ values. 2 points e. Use the standard error approach to find a 95% confidence interval for the parameter of interest. 5 points f. Using the percentile approach, find a 95% confidence interval for the parameter of interest. 3 points g. Interpret the 95% confidence interval you have provided as an answer to question 4f. 4 points h. Based on the confidence interval provided in 4f can you conclude with 95% confidence that the mean commute time for workers in the Atlanta area differs from the mean commute time for workers in metropolitan St. Louis? Briefly explain. 4 points

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Solution Part a The city Atlanta appears to have longer commute time due ... View the full answer