Latex allergy in health care workers. Refer to the Current Allergy & Clinical Immunology (March 2004) study of health care workers diagnosed with a latex allergy, Exercise 7.15

(p. 352). Consider testing the null hypothesis of m = 20 against the alternative hypothesis of m 6 20 using a = .01, where m is the mean number of latex gloves used per week. The sample of n = 46 workers had a standard deviation of s = 11.9. Assume s is a good estimate of the true standard deviation s.

a. Find the power of the test if the true mean is m = 19.

b. Repeat part a for the true mean values 18, 16, 14, and 12.

c. Plot the power of the test on the vertical axis against the alternative mean on the horizontal axis. Draw a curve through the points. What pattern do you observe?

d. Use the power curve, part

c, to estimate the power for the mean value m = 15. Calculate the power for this value of m, and compare it with your approximation.

e. If the true value of the mean number of latex gloves used per week is really 15, what is the probability that the test will fail to reject H0: m = 20?