Question

For healthy individuals the level of prothrombin in the blood is approximately normally distributed with mean 20 mg/100 mL and standard deviation 4 mg/100mL. Low levels indicate low clotting ability. In studying the effect of gallstones on prothrombin, the level of each patient in a sample is measured to see if there is a deficiency. Let µ be the true average level of prothrombin for gallstone patients.

a) What are the appropriate null and alternative hypothesis?

b.) Let Xbar denote the sample average level of prothrombin in a sample of n=20 randomly selected gallstone patients. Consider teh test procedure with test statistic Xbar and rejection region (small)xbar <= 17.92. What is the probability distribution of the test statistic when H0 is true? What is the probability of a type I error for the test procedure?

c.) What is the probability distribution of the test statistic when µ=16.7? Using the test procedure of part (b), what is the probability that hte gallstone patients will be judged not deficient in prothrombin, when in fact µ=16.7 (a type II error)?

d.) How would you change the test procedure of part (b) to obtain a test with significance level of .05? What impact would this change have on the error probability of part (c)?

e.) Consider the standardized test statistic Z= (Xbar - 20)/(sigma / sqrt( n ) ) = (Xbar - 20) /.8944. What are the values of Z corresponding to the rejection region of part (b)?

Answer 1