Question: A weight loss program claims that program participants have a mean weight loss of at least 10 pounds after one month. You work for a medical association and are asked to test this claim. A random sample of 30 program participants and their weight losses (in pounds) after one month is listed below.

5.7 5.7 6.6 6.7 7.0 7.1

7.9 8.2 8.2 8.7 8.9 9.0

9.3 9.5 9.6 9.8 10.2 10.5

10.6 10.6 11.1 11.2 11.5 11.7

11.8 12.0 12.7 12.8 13.8 15.0

a. Construct a relative frequency and a cumulative frequency distribution for the data.

b. Construct a relative frequency histogram and a relative frequency polygon for the data.

c. Find the point estimates for the population mean and the population standard deviation.

d. Construct a 95% confidence interval for the population mean.

e. At a= 0.05 and using p-values, do you have enough evidence to reject the program's claim? Interpret your results.