1.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 2403.7 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 2453.7 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 2403.7 calories a day.

(1)(2 points) Write out the hypotheses for this test in terms of , , and :

(2)(6 points) Using the hypothesis test written in part (1), conduct the test for the following situations (use :Include the test statistic, p-value, and decision (reject or don't reject ).

i.A sample of 100 athletes; the average caloric intake is

ii.A sample of 600 athletes; the average caloric intake is