Question

The Earth Wind and Fire love estimating sampling distributions using bootstrapping. They take a random sample of 11 of their fans and determine the IQ of each fan: 87, 95, 102, 110,93,96,117,89,98,100,105. Find the bootstrap distribution of the average IQ of Earth Wind and Fire fans using 10000 resamples and then find a 98% bootstrap percentile confidence interval for the average IQ of a Earth Wind and Fire.

Answer 1

The following are the steps to estimate sampling distrinbution of average IQ using Bootstrap

1. Get a sample of size 11 from the original sample of 11 IQs, with replacement
2. Calculate the sample average and store
3. Repeat 1 and 2 10000 times. These are bootstrap resamples
4. 98% confidence interval corresponds to significance level .
5. the 98% confidence interval is resampled averages at alpha/2*100 = 1st percentile and (1-alpha/2)*100=99th percentile

the following is the R code (all statements atrting with # are comments)

Get the following

Get the following histogram