A grocery store manager is interested in determining whether or not a difference exists between the shelf life of two different brands of doughnuts.A random sample of 100 boxes of each brand was selected and the shelf life in days was determined for each box.The difference in sample means is found to be $\bar { x } _ { 1 } - \bar { x } _ { 2 } = 0.8$ .Ten subsequent bootstrap samples from each of these original samples yield the following values of $\bar { x } _ { 1 } ^ { * } - \bar { x } _ { 2 } ^ { * }$ 1.8,2.7,-1.9,2.1,0.1,-0.5,-2.3,1.2,2.1,-1.0.Based on these ten values,find the bootstrap of the standard error of $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ .
A)1.7982
B)0.5686
C)3.2334
D)0.43
E)2.1111

Question

Quizplus · Accepted Answer

The bootstrap standard error is the standard deviation of the bootstrap distribution. The bootstrap distribution is the distribution of the bootstrap statistic, which is the difference between the sample means of the two bootstrap samples. The bootstrap statistic is calculated by taking a random sample with replacement from the original sample, and then calculating the difference between the sample means of the two bootstrap samples. The bootstrap standard error is calculated by taking the standard deviation of the bootstrap distribution. In this case, the bootstrap standard error is 1.7982.

A Grocery Store Manager Is Interested in Determining Whether or Not