28 Mar MAT 274 BENCHMARK FORMAT AND STYLE TEMPLATE

MAT 274 BENCHMARK FORMAT AND STYLE TEMPLATE

 

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:

a.     Once?

b.     n=#+2 times, where # is the last digit of your student ID?

c.     n=#+4 times, where # is the last digit of your student ID?

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

 

For each part, insert your sketch of the required area under the normal curve. In addition, include a screenshot of your Excel computation to find this area.

                                               i.     Insert screenshot and figure for part (a)

 

                                             ii.     Insert screenshot and figure for part (b)

 

                                           iii.     Insert screenshot and figure for part (c)

 

                                            iv.     Comment on the relationship among the probabilities in parts (a),(b), and (c).

 

 

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 (do NOT use Baye’s Theorem) and Conditional Probabilities to compute the following quantities based on the information given only in part 2:

a.     If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes?

b.     What is the probability of having the disease given that you test positive?

c.     If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes?

d.     What is the probability of having the disease given that you tested negative?

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

 

Fill in the conditional probability table here, then answer the questions in each part below.

 

	Test positive	Test Negative	Total
Have Gest Diabetes
Don’t have Gest Diabetes
Total			100,000

 

                                               i.     Answer part (a) here.

 

                                             ii.     Answer part (b) here.

 

                                           iii.     Answer part (c) here.

 

                                            iv.     Answer part (d) here.

 

                                             v.     Comment on how prevalence of the disease affects your ability to trust the test. Discuss what factors would lead you to trust the blood test, or not trust the blood test. HINT: If EVERYONE had Gest Diabetes, how many false positives/negatives would you have? If NOBODY had Gest Diabetes, how many false positives/negatives would you have? Compare these to the actual table results for your #.

 

 

 

3.     UPDATED – Use this version! From part 2 of this assignment, you know that gestational diabetes affects #+1 percent of the population in our patient’s age group. Many women in this age group have decided to follow a special diet, which is advertised as being especially nutritious for the baby. One  clinic has 53 pregnant women who have elected to follow this diet. Out of these women, #+3 percent of them  have developed  gestational diabetes.  Use a 5% significance level to determine if this rate is higher than the #+1 percent level in the general population.  Show all work and include screen shots of any Excel template pages you use. Include the following.

 

a.     A formal statement of the null and alternative hypothesis for your test. Make sure to include correct statistical notation for the formal null and alternative, do not just state this in words.

 

b.     Screen shots of any Excel Template pages you use.  

 

 

c.     An interpretation of your p-value including

                                               i.     A statement saying whether you reject or fail to reject the Null Hypothesis, and why  (what statistical results led you to your result)

 

 

                                             ii.     A few sentences in language that someone in the general public would understand to explain your conclusion. For example, consider what you would say if you were a healthcare provider in this clinic and one of the patients came to you, asking you if this diet was unhealthy?