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Consider the probabilistic modeling for following four data sets. For which data set would a mixture model be most appropriate?

100 individuals have received a test for covid-19 virus. Here are the results: 15 have the virus and test positive. 5 have the virus and test negative. 78 don’t have the virus and test negative. 2 don’t have the virus and test positive.  The true positive rate of the test in this sample is 

What is the action of all of the negative feedback mechanisms of the body?

Which of the following should NOT be used as a null hypothesis?

Consider the following violin plot for the chickwts dataset. Which feed group below has the smallest average weight? 

Consider the following code: ggplot(data = DNase, mapping = aes(x = conc, y = density)) + geom_point() + geom_smooth() Which of the following best describes what this code produces?

Consider Question 14. We can view the anemia diagnosis as a hypothesis testing problem. The null hypothesis is that the women does not have anemia, and we know that a small hemoglobin level tends to suggest anemia. Suppose a women has hemoglobin level = 10. What is the corresponding p-value?

Suppose we have the counts of A, T, C, G in chromosome 1 of some individual. Denote them by  nA, nT, nC, nG.  Our goal is to check whether the A-T and C-G base pairing rule exists in human genome by hypothesis testing. Which of the following is the best choice for the test statistic? (Note that |x| denotes the absolute value of x.)

The cranial cavity contains the brain.