. A patient is classified as having gestational diabetes if their 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 withμ= 140+#mg/dlandσ= #+1 mg/dl, where # is the last digit of your GCU student ID number. What is the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:
- n=#+2 times, where # is the last digit of your student ID?
- n=#+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 lecture 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 9X percent reliable, gestational diabetes affects X+1 percent of the population in our patient’s age group, and that our test has a false positive rate of X+4 percent. Compute the following quantities based on this new information:
- If 100,000 people take the blood test, how many people that test positive will 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 that 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 the following:
- A detailed discussion of your experimental design. Detailed experimental design should include the type of experiment, how you chose your sample size, what data is being collected, and how you would collect that data.
- How is randomization used in your sampling or assignment strategy? Remember to discuss how you would randomize for sampling and assignment, what type of randomization are you using?
- The type of inferential test utilized in your experiment. Include type of test used, number of tails, and a justification for this choice.
- 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.
- A confidence interval for estimating the parameter in your test. State and discuss your chosen confidence level, why this is appropriate, and interpret the lower and upper limits.
- An interpretation of your p-value and confidence interval, including what they mean in the context of your experimental design. Answer each part below. State your significance level, interpret your p-value, and make a decision on the null.
This assignment uses a rubric and it should be reviewed before submission to ensure all expectations are being met.
APA style is not required, but solid academic writing is expected.
You are not required to submit this assignment to LopesWrite.
This benchmark assignment assesses the following programmatic competencies:
B.S. Math Sec. Ed.
6.1 Students will examine the sources of statistical viability and the role randomness in statistical inference.
6.2 Students will be able to select the appropriate probability distribution for a variety of data sets and estimate the parameters.
6.3: Students will be able to develop and perform the most appropriate test of hypothesis using a variety of experimental designs.
6.4 Students will be able to construct a sufficient representation of a variety of data sets.
6.5 Students will be able to distinguish between empirical and theoretical probability and the impact on calculations of probability.