QUESTION 2 

(a) Suppose that an allergist (a physician specializing in the diagnosis and treatment of allergies) wishes to test the hypothesis that at least 30% of the public is allergic to some cheese products. Explains how the allergist could commit a type I error.

(b) Past experience indicates that the time required for students in a university to complete a standardize test is a normal random variable with a mean of 35 minutes. If a random sample of 20 students took an average of 33.1 minutes to complete the test with a standard deviation of 4.3 minutes, test the hypothesis, that the average time taken is actually less than 35 minutes. 

(i) State your hypothesis null, H0 and hypothesis alternative, H1.

(ii) Test the hypothesis given in (i) at the 0.05 significance level. Do you reject or fail to reject the H0? State your conclusion.

(c) Shown below are birth weights (in kilograms) of male babies born to mothers taking a special vitamin supplement. Test the claim that this sample comes from a population with a standard deviation equal to 0.470kg, which is the standard deviation for male birth weights in general. At α = 0.05, does the vitamin supplement appear to affect the variation among birth weights?

3.73        4.37        3.73        4.33        3.39        2.47        4.47        3.43 

3.68        4.68        3.52        3.02        4.09        4.13        3.22        2.54

(i) State H0 and H1.

(ii) Calculate the test statistics. 

(iii) Find the critical value.

(iv) Test the claim whether the vitamin supplement appear to affect the variation among birth weights. State your conclusion.