A blood test is used to detect Lyme disease. Consider the following facts: • About 0.207% of the population has Lyme disease • 99.793% of the population does not have Lyme disease • 93.7% of those with Lyme disease will test positive if given the blood test. • 6.3% of those with Lyme disease will test negative if given the blood test. • 3% of those who do not have Lyme disease will test positive if given the blood test. • 97% of those who do not have Lyme disease will test negative if given the blood test. a. Suppose a random person is selected and given the blood test. What is the probability that they test positive? (5 pts) b. Suppose a random person is selected and given the blood test and they test positive. What is the probability that they have Lyme disease? (5 pts)
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Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county in the United States. $$\begin{array}{lcccccccccccc} \text { Month } & \mathbf{J} & \mathbf{F} & \mathbf{M} & \mathbf{A} & \mathbf{M} & \mathbf{J} & \mathbf{J} & \mathbf{A} & \mathbf{S} & \mathbf{O} & \mathbf{N} & \mathbf{D} \\ \hline \begin{array}{l} \text { Cases } \\ \text { of Lyme } \\ \text { Disease } \end{array} & 3 & 2 & 2 & 4 & 5 & 15 & 22 & 13 & 6 & 5 & 4 & 1 \\ \hline \text { Drowning } & & & & & & & & & & & & \\ \text { Dcaths } & 0 & 1 & 2 & 1 & 2 & 9 & 16 & 5 & 3 & 3 & 1 & 0 \end{array}$$ (a) Draw a scatter diagram of the data using cases of Lyme disease as the explanatory variable. (b) Compute the correlation coefficient for the data. (c) Based on your results from parts (a) and (b), what type of relation exists between the number of reported cases of Lyme disease and drowning deaths? Do you believe that an increase in cases of Lyme disease causes an increase in drowning deaths? What is a likely lurking variable between cases of Lyme disease and drowning deaths?
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A new screening test for Lyme disease has been developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Three hundred people are screened at a clinic during the first year the new test is implemented. (Assume the true prevalence of Lyme disease among clinic attendees is 10%.) Calculate the following values: The predictive value of a positive test is: A. 33.0% B. 18.2% C. 94.0% D. 22.2% E. 6.0%
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