# This exercise continues the study of the robustness of the Student’s t method for constructing…

This exercise continues the study of the robustness of the Student’s t method for constructing confidence intervals. The following figure shows graphs of probability density functions for the N(0, 1) distribution, the lognormal distribution with &#120583; = 1 and &#120590;2 = 0.25, and the gamma distribution with r = 0.5 and &#120582; = 0.5 (this is also known as the chi-square distribution with one degree of freedom). For each of these distributions, generate 10,000 samples of size 5, and for each sample compute the upper and lower limits of a 95% confidence interval using the Student’s t method. [If necessary, it is possible to compute the lognormal and gamma random values from normal random values. Specifically, to compute a value X from a lognormal distribution with &#120583; = 1 and &#120590;2 = 0.25, generate Y ∼ N(1, 0.25) and compute X = eY . To generate a value X from a gamma distribution with r = 0.5 and &#120582; = 0.5, generate Y ∼ N(0, 1) and compute X = Y2.]

a. The true mean of the N(0, 1) distribution is 0. Based on the simulation results, estimate the coverage probability (proportion of samples for which the confidence interval covers the true mean) for samples of size 5 from the N(0, 1) distribution. (Since the assumptions underlying the Student’s t method are satisfied here, your answer should be very close to 95%.)

b. The true mean of the lognormal distribution with &#120583; = 1 and &#120590;2 = 0.25 is 3.0802. Based on the simulation results, estimate the coverage probability (proportion of samples for which the confidence interval covers the true mean) for samples of size 5 from the lognormal distribution with &#120583; = 1 and &#120590;2 = 0.25.

c. The true mean of the gamma distribution with r = 0.5 and &#120582; = 0.5 is 1. Based on the simulation results, estimate the coverage probability (proportion of samples for which the confidence interval covers the true mean) for samples of size 5 from the gamma distribution with r = 0.5 and &#120582; = 0.5.

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.
Psychology
quick and before due date/time.
Customer 453027, January 29th, 2022
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
English 101
Thank you for this excellent analysis of the Alchemist.
Customer 453213, June 15th, 2022
awesome job
Customer 453201, June 24th, 2022
Nursing
thank you so much
Customer 452749, June 10th, 2021
Psychology
Customer 453027, January 15th, 2022
Health Care
awesome work
Customer 452777, October 14th, 2021
Psychology
Came in as promissed. Good paper.
Customer 453027, January 6th, 2022
excellent work
Customer 453201, November 1st, 2022
History
Looks great and appreciate the help.
Customer 452675, April 26th, 2021
Social Work and Human Services
Great work I would love to continue working with this writer thought out the 11 week course.
Customer 452667, May 30th, 2021
Humanities
Thank youuuu
Customer 452729, May 30th, 2021
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend