10.9 Millions of dollars are spent each yr on diet foods. Trends such as the low fat diet or the low carb Atkins diet have led to a host of new product. A study by Dr. Linda Stern of the Philadelphia VA Hospital compared weight loss between obese patients on a low fat diet and obese patients on a low carb diet. Let Âľ1 represent the mean number of pounds obese patients on a low fat diet lose in six months and Âľ2 represent the mean number of pounds obese patients on a low carb diet lose in six months.

a. State the null and alternative hypothesis if you want to test whether the mean weight loss between the two diets is equal.
b. In the context of this study, what is the meaning of a Type I error?
c. In the context of this study, what is the meaning of a Type II error?
d. Suppose that a sample of 100 obese patients on a low fat diet lost a mean of 7.6 pounds in six months, with a standard deviation of 3.2 pounds, while a sample of 100 obese patients on a low carb diet lost a mean of 6.7 lbs. in 6 mths., with a standard deviation of 3.9 lbs. Assuming that the population variances are equal and using a .05 level of significance, is there evidence of a difference in the mean weight loss of obese patients between the low fat and low carb diets?

10.51
A bank with a branch located in a commercial district of a city has developed an improved process for serving customers during the noon to 1pm lunch period. The waiting time (operationally defined as the time elapsed from when the customer enters the line until he or she reaches the teller window) of all customers during this hour is recorded over a period of one week. A random sample of 15 customers is selected and the results are as follows:

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20

4.50 6.10 0.38 5.12 6.46 6.19 3.79
Suppose that another branch, located in a residential area, is also concerned with the noon to 1pm lunch period. A random sample of 15 customers is selected and the…