Question

The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Five adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are

Person                                       1          2          3          4         5

Weight before the diet             180      125      240      150      160

Weight after six weeks             165      126      230      149      140

Is there evidence that the diet leads to weight loss?

a. Check the needed conditions for both the test statistic and confidence interval. (Do not do a stemplot.)

b. State Ho and Ha

c. Calculate the test statistic (if applicable – state the degrees of freedom)

d. Find the p-value

e. What is the conclusion for this problem? Do you reject Ho?

f. Calculate the 99% confidence interval.

g. Interpret the confidence interval

Answer 1

a)

The needed conditions for both the test statistic and the confidence interval is that the difference that is d=Weight before the diet (X1)- Weight after six months (X2) is followed a normal distribution. From the above graph, we can conclude that the difference is to follow the required normal distribution at 0.05 level of significance.

g) The confidence interval in f) include the value zero. Hence, we can conclude that there is no evidence that the diet leads to weight loss at the 0.01 level of significance.