25. The water diet requires one to drink two cups of water every half hour from

ID: 3318466 • Letter: 2

Question

25. 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 wees. Fue 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 The weights (in pounds) are Weight before the diet 180 130 | 240 150 202 Weight after six weeks on the diet 170 130 215 | 149 | 190 Weight loss: (Before) - (After) For the population of all adults, assume that the weight loss after six weeks on the diet (weight before the diet minus weight after six weeks on the diet) is Normally distributed with unknown mean u. We do a test of significance to determine if the sample provides sufficient evidence that the water diet causes weight loss. (Ha: average weight loss is greater than 0.) What is the t-test statistic in the test? a. 0.051 b. 2.373 c. 1.898 d. 0.425 e. 2.122

Explanation / Answer

Solution:

Here, we have to find the t test statistic for paired t test.

Test statistic formula is given as below:

t = Dbar / [Sd/sqrt(n)]

Where, Dbar is the mean of differences, Sd is the standard deviation of differences, and n is sample size.

From given data, we have

No.

Before

After

(Di - Dbar)^2

180

170

0.16

130

92.16

240

215

237.16

150

149

73.96

202

190

5.76

Total

902

854

409.2

Dbar = 48/5 = 9.6

Variance = (Di - Dbar)^2/(n – 1) = 409.2 / (5 – 1) = 409.2/4 = 102.3

Sd = sqrt(102.3) = 10.11434625

t = 9.6/[10.11434625/sqrt(5)]

t = 2.1224

Correct Answer: e.2.122

No.