A consumer advocate is comparing income for a wide variety of jobs between the South and the Northeast.The average income of a simple random sample of 800 jobs in the Northeast is compared to the average income of a simple random sample of 750 jobs in the South.From the collected data,950 resamples are taken.Each time,750 incomes are selected with replacement from the data collected from the South,and 800 incomes are selected with replacement from the data collected from the Northeast.The distribution of the difference in means based on the resamples is shown below (in thousands of dollars). Based on the graph,which of the following 95% bootstrap intervals is best to use to estimate the difference in mean income?
A)The bootstrap t interval
B)The bootstrap percentile interval
C)The BCa interval
D)Because the samples were large,we can use any of the above.

Question

A consumer advocate is comparing income for a wide variety of jobs between the South and the Northeast.The average income of a simple random sample of 800 jobs in the Northeast is compared to the average income of a simple random sample of 750 jobs in the South.From the collected data,950 resamples are taken.Each time,750 incomes are selected with replacement from the data collected from the South,and 800 incomes are selected with replacement from the data collected from the Northeast.The distribution of the difference in means based on the resamples is shown below (in thousands of dollars).  Based on the graph,which of the following 95% bootstrap intervals is best to use to estimate the difference in mean income?
A)The bootstrap t interval 
B)The bootstrap percentile interval 
C)The BCa interval 
D)Because the samples were large,we can use any of the above.

Quizplus · Accepted Answer

The bootstrap BCa interval is the best choice because it takes into account both the skewness and bias of the distribution, which is evident in the graph. The bootstrap t interval assumes normality, which is not a safe assumption in this case, and the bootstrap percentile interval does not take into account bias. Therefore, the BCa interval provides a more accurate estimate of the difference in means.

A Consumer Advocate Is Comparing Income for a Wide Variety