Statistics & Probability Questions Worksheet.

1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca’s doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca’s measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with *μ*= 140+# mg/dl and *σ* = #+1 mg/dl, where # is the last digit of your GCU student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:

- Once?
- #+2 times, where # is the last digit of your student ID?
- #+4 times, where # is the last digit of your student ID?

Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from the reading why this occurs and what it means in context.

2. Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 9# percent reliable, this means that the test will yield an accurate positive result in 9#% of the cases where the disease is actually present. Gestational diabetes affects #+1 percent of the population in our patient’s age group, and that our test has a false positive rate of #+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2:

- If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes?
- What is the probability of having the disease given that you test positive?
- If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes?
- What is the probability of having the disease given that you tested negative?

Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?

3. As we have seen in class, hypothesis testing and confidence intervals are the most common inferential tools used in statistics. Imagine that you have been tasked with designing an experiment to determine reliably if a patient should be diagnosed with diabetes based on their blood test results. Create a short outline of your experiment, including all of the following:

- A detailed discussion of your experimental design.
- How is randomization used in your sampling or assignment strategy?
- The type of inferential test utilized in your experiment.
- A formal statement of the null and alternative hypothesis for your test.
- A confidence interval for estimating the parameter in your test.
- An interpretation of your p-value and confidence interval, including what they mean in context of your experimental design

*NOTE: USE THE ATTACHED EXCEL SHEET TO GENERATE YOUR VALUES FOR EACH PART OF THE PROJECT!

This assignment uses a rubric and it should be reviewed before submission to ensure all expectations are being met.

MAT 274 BENCHMARK FORMAT AND STYLE TEMPLATE

1attachments

Slide 1 of 1

- attachment_1attachment_1

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
## Recent Comments