Analyze the factorial effects and comment on the effects that are important.

Question

3. Bayesian Inference – Updating Beliefs A medical test for a rare disease has the following characteristics: Sensitivity (true positive rate): 99% Specificity (true negative rate): 98% The disease occurs in 0.5% of the population. A patient receives a positive test result. Questions: a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.

Answer 1

Question

Chapter 14, Problem 98SE

a.

To determine

Analyze the factorial effects and comment on the effects that are important.

b.

To determine

Develop a regression model to predict the response in terms of actual factor levels.

c.

To determine

Check whether the residual analysis indicate any problems.

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