Residents of large urban cities often complain about the lack of parking and overpriced parking tickets.The mayor of Washington,DC,is doing a study to find out the 25% trimmed mean of all parking tickets received by residents in 1 year.A sample of 50 residents yielded a 25% trimmed mean of $150.00 and the bootstrap standard error is $23.00.What is the 95% bootstrap confidence interval for the 25% trimmed mean?
A)(104,196)
B)(102.62,197.38)
C)This cannot be computed from the given information.
D)None of the above

Question

Quizplus · Accepted Answer

Using the bootstrap method, we can construct the confidence interval as follows:

- Generate a large number of bootstrap samples from the original sample.
- For each bootstrap sample, calculate the 25% trimmed mean.
- Calculate the standard error of the bootstrap mean by taking the standard deviation of the bootstrap means.
- Construct the confidence interval using the formula: 
trimmed mean ± (Zα/2 × SE)
where Zα/2 is the critical value of the standard normal distribution for the desired confidence level (95% in this case), and SE is the standard error of the bootstrap mean.

From the given information, we know that the 25% trimmed mean of the sample is $150.00, and the bootstrap standard error is $23.00. We also know that the confidence interval should be based on the 25% trimmed mean, not the untrimmed mean.

Using a standard normal distribution table or calculator, we can find that the critical value for a 95% confidence interval is Zα/2 = 1.96.

Therefore, the 95% bootstrap confidence interval for the 25% trimmed mean is:
150.00 ± (1.96 × 23.00) or (102.62, 197.38)

So the correct answer is B.

Residents of Large Urban Cities Often Complain About the Lack