The weekly weight losses of all dieters on Diet I have a normal distribution with a mean of 1.3 pounds and a standard deviation of .4 pound. The weekly weight losses of all dieters on Diet II have a normal distribution with a mean of 1.5 pounds and a standard deviation of .7 pound. A random sample of 25 dieters on Diet I and another sample of 36 dieters on Diet II are observed.
a. What is the probability that the difference between the two sample means, 1 – 2, will be within –.15 to .15, that is, –.15 < 1 – 2 < .15?
b. What is the probability that the average weight loss 1 for dieters on Diet I will be greater than the average weight loss 2 for dieters on Diet II?
c. If the average weight loss of the 25 dieters using Diet I is computed to be 2.0 pounds, what is the probability that the difference between the two sample means, 1 – 2 will be within –.15 to .15, that is, –.15 < 1 – 2 < .15?
d. Suppose you conclude that the assumption –.15 < µ1 – µ2 < .15 is reasonable. What does this mean to a person who chooses one of these diets?