# Practice Midterm Exam (Statistics)

## Instructions

This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete solutions for full credit. Good luck!

In a study of hypnotic suggestion, 5 male volunteers participated in a two-phase experimental session. In the first phase, respiration was measured while the subject was awake and at rest.

In the second phase, the subject was told to imagine that he was performing muscular work, and respiration was measured again. Hypnosis was induced between the first and second phases; thus, the suggestion to imagine muscular work was “hypnotic suggestion” for these subjects. The accompanying table shows the measurements of total ventilation (liters of air per minute per square meter of body area) for all 5 subjects.

## Experimental Group

 Subject Rest Work 1 6 6 2 7 9 3 8 9 4 7 10 5 6 7

Use suitable test to investigate whether there is any difference between the two experimental phases in terms of total ventilation. Please state the assumption(s) of the test and report the p-value. At the significance level of 0. 05, what is your conclusion?  Please write up the entire SAS program necessary to answer questions raised in (a). Please include the data step as well as tests for testing for various assumptions.

John Pauzke, president of Cereals Unlimited, Inc. , wants to be very certain that the mean weight of packages satisfies the package label weight of 16 ounces. The packages are filled by a machine that is set to fill each package to a specified weight. However, the machine has random variability measured by John would like to have strong evidence that the mean package weight is above 16 ounces.

George Williams, quality control manager, advises him to examine a random sample of 25 packages of cereal. From his past experience, George knew that the weight of the cereal packages follows a normal distribution with standard deviation 0. 4 ounce. At the significance level ? =. 05, (1) What is the decision rule (rejection region) in terms of the sample mean. Please derive the general formula using the concept of Type I error rate.  What is the power of the test when ? =16. 2 ounces? Please derive the general formula for power calculation first.

What is the sample size necessary to ensure a power of 80% when ? =16. 2 ounces. Please derive the general formula for sample size calculation based on the Type I and II error rates first.

## Solution

Hence, about 25 packages of cereal should be sampled to achieve a power of 80% when (=16. 2 ounces. 3a (for all except AMS PhD students). Inference on one population mean when the population is normal, and the population variance is known.

Let be a random sample from the given normal population. For a random sample from any population for which the mean and variance exist. Please prove that

1. The sample mean and sample variance are unbiased estimators of the population mean and variance respectively.
2. When the population is normal, we have learned that the sample mean and the sample variance, are indeed, independent.

Please prove this for n = 2. That is, for a random sample of size 2 only. An expert witness in a paternity suit testifies that the length (in days) of pregnancy (that is, the time from impregnation to the delivery of the child) is approximately normally distributed.

The defendant in the suit is able to prove that he was out of the country during a period that began 290 days before the birth of the child and ended 240 days before the birth. If the defendant was, in fact, the father of the child, what is the probability that the mother could have had the very long or very short pregnancy indicated by the testimony?

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 MyhomeworkGeeks
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.
fin571
EXCELLEN T
Customer 452773, March 21st, 2024
FIN571
excellent
Customer 452773, March 15th, 2024
Nursing
I just need some minor alterations. Thanks.
Customer 452547, February 10th, 2021
DATA565
The support team was late responding , my paper was late because the support team didn't respond in a timely manner. The writer of the paper finally got it right but seems there was a problem getting the revisioin to me.
Customer 452773, April 7th, 2024
Thank you very much for a good job done and a quick turn around time.
Customer 452615, March 31st, 2021
FIN571
excellent work
Customer 452773, March 1st, 2024
always perfect work and always completed early
Customer 452773, February 21st, 2023
Thank you for your hard work and help.
Customer 452773, February 13th, 2023
Thanks
Customer 452773, March 3rd, 2023
History
Don't really see any of sources I provided, but elsewise its great, thank you!
Customer 452697, May 8th, 2021
Customer 452773, March 22nd, 2023
Human Resources Management (HRM)
excellent work
Customer 452773, July 3rd, 2023
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat