4. Of those women who are diagnosed to have early-stage breast cancer in a certain community, it is assumed that one-fourth will die of the disease. Suppose a community public health department instituted a screening program to provide early detection of breast cancer and to increase the survival rate p of those diagnosed to have the disease. A random sample of 250 women was selected from among those who were periodically screened by the program and who were diagnosed with the disease. Let X represent the number of those in the sample who survive the disease. (1) (1 point) If you wish to determine whether the community screening program has been effective, state the alternative hypothesis that should be tested. (2) (1 point) State the null hypothesis. (3) (4 points) if X = 224 women in the sample of 250 survive the disease, can you conclude that the community screening program was effective? Calculate the test statistic and p-value, and use a = 0.05 to state your final conclusion. 5. Every user of statistics should understand the distinction between statistical significance and practical (or clinical) significance. A sufficiently large sample will declare very small effects statistically significant. Consider the study of elite Canadian female athletes. Female athletes were consuming an average of 2503.7 kcal/day with a standard deviation of 880 kcal/day. Suppose a nutritionist is brought in to implement a new health program for these athletes. This program should increase mean caloric intake but not change the standard deviation. Given the standard deviation and how caloric deficient these athletes are, a change in the mean of 50 kcal/day to 2553.7 is of little importance. However, with a large enough sample, this change can be significant. Assume an investigator is wanting to test the hypothesis that female athletes consume on average more than 2503.7 calories a day. (1) (2 points) Write out the hypotheses for this test in terms of Ho, HA, and u: (2) (6 points) Using the hypothesis test written in part (1), conduct the test for the following situations (use a = 0.10): Include the test statistic, p-value, and decision (reject or don't reject Ho). i. A sample of 100 athletes; the average caloric intake is x = 2553.7 ii. A sample of 500 athletes; the average caloric intake is x = 2553.7