The following table lists the weight of individuals before andafter taking a diet prescribed by a weight-loss company for amonth:

Weight-loss Data:

Individual: A, B, C, D, E, F

Weight Before (lb): 123.7, 128.7, 135.6, 194.9, 145.5, 162.3

Weight After (lb): 109.4, 109.7, 123.3, 186.5, 126.8, 151.5

Weight loss (lb): 14.3, 19.0, 12.3, 8.4, 18.7, 10.8

You may find this Student's t distribution table useful inanswering the following questions. You may assume that thedifferences in weight are normally distributed.

a)Calculate the sample variance (sd2) of the changes inindividual weights. Give your answer to 2 decimal places.

sd2 =

b)A disgruntled customer states: "This weight-loss company is acomplete farce. All the people I know who signed up experienced nochanges in their weight at all. I seriously doubt this diet has anyeffect whatsoever. I want my money back!"

You plan to do a hypothesis test on this claim where thehypotheses are:

H0: the customer's claim is true and the program has no effecton weight

HA: the customer's claim is not true and the program does havean effect on weight, whether it increases or decreases

According to the data given, you should accept, reject,or not reject the null hypothesis at a confidence level of99%.