# A general method for finding a confidence interval for the difference between two means of normal…

A general method for finding a confidence interval for the difference between two means of normal populations is given by expression (5.21) on page 366. A pooled method that can be used when the variances of the populations are known to be equal is given by expression (5.22) on page 368. This exercise is designed to compare the coverage probabilities of these methods under a variety of conditions. A fair amount of coding may be required, depending on the software used.

a. Let nX = 10, nY = 10, &#120590;X = 1, and &#120590;Y = 1. Generate 10,000 pairs of samples: X∗ 1 , …, X∗ nX from a N(0, &#120590;2 X) distribution, and Y∗ 1 , … , Y∗ nY from a N(0, &#120590;2 Y ) distribution. For each pair of samples, compute a 95% confidence interval using the general method, and a 95% confidence interval using the pooled method. Note that each population has mean 0, so the true difference between the means is 0. Estimate the coverage probability for each method by computing the proportion of confidence intervals that cover the true value 0.

b. Repeat part (a), using nX = 10, nY = 10, &#120590;X = 1, and &#120590;Y = 5.

c. Repeat part (a), using nX = 5, nY = 20, &#120590;X = 1, and &#120590;Y = 5.

d. Repeat part (a), using nX = 20, nY = 5, &#120590;X = 1, and &#120590;Y = 5.

e. Does the coverage probability for the general method differ substantially from 95% under any of the conditions in parts (a) through (d)? (It shouldn’t.)

f. Based on the results in parts (a) through (d), under which conditions does the pooled method perform most poorly?When the sample sizes are equal and the variances differ. When both the sample sizes and the variances differ, and the larger sample comes from the population with the larger variance. When both the sample sizes and the variances differ, and the smaller sample comes from the population with the larger variance.

Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with My Study Writers
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Education
Very fast response and did a excellent job.
Customer 453201, May 31st, 2022
Human Resources Management (HRM)
On time and as always a great service! This semester has been very time consuming a tough for my family so this service has not only been a life saver but helped me keep up my grades! If you are in a time crunch or need help, don't hesitate! They are worth it!
Customer 453077, April 4th, 2022
Other
Thank you , Excellent work
Customer 453201, June 2nd, 2022
Economics
For some reason I did not get an email that the order was done, but it was on time regardless
Customer 453291, October 16th, 2022
excellent work
Customer 453201, November 1st, 2022
Sociology
THANK YOUUUUU
Customer 452591, March 18th, 2021
excellent
Customer 453201, October 22nd, 2022
Literature
Thank you!
Customer 453145, April 19th, 2022
Nursing
Thank you so much for your help! :)
Customer 453167, May 11th, 2022
Humanities
Thank youuuu
Customer 452729, May 30th, 2021
Human Resources Management (HRM)
Always great! My son has been in critical health these last few semesters. Many times I have thought he wasn't going to make it and thought about quitting or postponing school until he was healthier but it always happens to be in the middle of the semester. This service has been a lifesaver for my mindset in helping keep my grades up and keep my son alive at the same time. I don't know if I could have made it through this period without it.
Customer 453077, June 6th, 2022
Nursing
Impressive writing
Customer 452547, February 6th, 2021
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend