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. What is the hypothesis of interest?

a. Write out the hypothesis test in terms of :

b. Using the hypothesis test written in part a, conduct the test for the following situations (use :

(1) A sample of 100 athletes; the average caloric intake is

(2) A sample of 1000 athletes; the average caloric intake is

2. A test of the null hypothesis  results in the test statistic .

(1) What is the p-value if the alternative is ?       

(2) What is the p-value if the alternative is ?           

(3) What is the p-value if the alternative is ?

3. A recent study looked to estimate the U.S. per capita consumption of sugar-sweetened beverages among adults aged 20 to 34 years. A random sample of 900 adults aged 20 to 34 is taken and has a mean sugar-sweetened beverage consumption of 338 kilocalories per day (kcal/d). Suppose that the population distribution is heavily skewed with a standard deviation of 300 kcal/d. 

(1) Give a 95% confidence interval for the true mean kilocalories consumed per day.

(2) How large of a sample must be taken to get a margin of error of  with 95% confidence?