THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
To investigate the effectiveness of a diet,a random sample of 16 female patients is drawn from a population of adult females using the diet.The weight of each individual in the sample is taken at the start and at the end of the diet.Assume that the population of differences in weight before and after the diet follows a normal distribution.Suppose the mean decrease in weights over all 16 subjects in the study is 4.0 pounds with the standard deviation of differences computed as 6.4 pounds.Let µ x - µ y = mean weight before the diet - mean weight after the diet.
-In order to test if the diet is effective,what is the value of the test statistic?
A)2.5
B)2.0
C)1.8
D)1.3

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
To investigate the effectiveness of a diet,a random sample of 16 female patients is drawn from a population of adult females using the diet.The weight of each individual in the sample is taken at the start and at the end of the diet.Assume that the population of differences in weight before and after the diet follows a normal distribution.Suppose the mean decrease in weights over all 16 subjects in the study is 4.0 pounds with the standard deviation of differences computed as 6.4 pounds.Let µ x - µ y  = mean weight before the diet - mean weight after the diet.
-In order to test if the diet is effective,what is the value of the test statistic?
A)2.5
B)2.0
C)1.8
D)1.3

Quizplus · Accepted Answer

The test statistic is calculated using the formula: $ \frac{\bar{x} - \mu}{(\frac{s}{\sqrt{n}})} $, where $ \bar{x} $ is the sample mean, $ \mu $ is the population mean (assumed to be 0 if we are testing for a mean decrease), $ s $ is the sample standard deviation, and $ n $ is the sample size. Plugging in the values: $ \frac{4.0 - 0}{(6.4/\sqrt{16})} = \frac{4.0}{1.6} = 2.5 $.