Question

Use the information on the percentiles from a bootstrap distribution of the mean commute distance of Pullman citizens to answer the questions that follow.

0.5% 1.0% 2.0% 2.5% 5.0% 95.0% 97.5% 98.0% 99.0% 99.5%

Percentile −0.945 −0.940 −0.931 −0.928 −0.919 −0.741 −0.723 −0.717 −0.705 −0.689

(a) Estimate a 95% Confidence Interval and interpret your results.

(c) Estimate a 90% Confidence Interval and interpret your results.

Answer 1

Percentile	0.50%	1%	2%	2.50%	5%	95%	97.50%	98%	99%	99.50%
Value of Percentile	-0.945	-0.94	-0.93	-0.928	-0.919	-0.741	-0.723	-0.717	-0.705	-0.689

The P% confidence interval is given by the value of the middle of p% of the bootstrap sample

i. 95% Confidence Interval is given by {2.50, 95.50 } [ In the given example keep the middle 95% and leaving 2.5% in each tail}

The 95% Confidence Interval is given by {-0.928 , -0.723}.i.e. We are 95% confident that mean commute distance of Pullman citizens lies between {-0.928, -0.723}

i. 90% Confidence Interval is given by {5, 95} [ In the given example keep the middle 90% and leaving 5% in each tail}

The 90% Confidence Interval is given by {-0.919, -0.741}.i.e. We are 90% confident that mean commute distance of Pullman citizens lies between {-0.919, -0.741}