Question

A study was conducted in order to compare the weight loss for two diet plans, Plan A and Plan B. Two hundred dieters were randomly selected. Of this sample 100 were placed on the Plan A diet and the remaining 100 were assigned to the Plan B diet. After the dieters were on the diet for 2 months the average weight loss and sample standard deviation of the weight losses were recorded. For the Plan A group there was an average weight loss of 10 lbs. with a standard deviation of √12, while the Plan B group had and average weight loss of 7 lbs. with a standard deviation of √13. Let ?1 denote the population average2 –month weight loss for dieters on Plan A, and let ?2 denote on the population average 2-month weight loss for dieters Plan B.

19) Referring to Diets, give the point estimate of ?1 − ?2.

a) -2 b) 10 c) 17 d) 3 e) 12

20) Referring to Diets, give the 90% confidence interval for ?1 − ?2.

a) 2.18 ≤ ?1 − ?2 ≤ 3.82 b) 2.02 ≤ ?1 − ?2 ≤ 3.98 c) 2.14 ≤ ?1 − ?2 ≤ 3.86 d) 2.36 ≤ ?1 − ?2 ≤ 3.64 e) 2.43 ≤ ?1 − ?2 ≤ 3.57

Answer 1

The statistical software output for this problem is:

On the basis of above output:

19. Point estimate = 3; Option D is correct.

20. 90% confidence interval:

2.18 ≤ ?1 − ?2 ≤ 3.82

Option A is correct.