11. Early Detection of Breast Cancer Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Suppose a screening program for the early detection of breast cancer was started in order to increase the survival rate p of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were screened by the program and who were diagnosed to have the disease. Let x represent the number of those in the sample who survive the disease.

a. If you wish to determine whether the screening program has been effective, state the alternative hypothesis that should be tested.

b. State the null hypothesis.

c. If 164 women in the sample of 200 survive the disease, can you conclude that the screening program was effective? Test using a 5.05 and explain the practical conclusions from your test.

d. Find the p-value for the test and interpret it.