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 appropriate critical value(s)at the 0.05 level of significance?
A)2.131
B)2.120
C)1.753
D)1.746

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 appropriate critical value(s)at the 0.05 level of significance?
A)2.131
B)2.120
C)1.753
D)1.746

Quizplus · Accepted Answer

The appropriate test here is a paired t-test with n-1 degrees of freedom (df = 15). For a two-tailed test at the 0.05 significance level with 15 degrees of freedom, the critical t-value is approximately 2.131. However, since the question asks for the critical value for a one-tailed test (testing if the diet is effective implies a one-tailed test), the critical value is approximately 1.753.