A researcher believes a new diet should improve weight gain.To test his hypothesis, a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected.The selected people on the old diet gained an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds.Assuming that the values are normally distributed in each population, the researcher would like to use the t procedure with pooled standard deviation.To use this procedure, it must be shown that the variances from the two populations can be assumed to be equal.Using the sample data to test this assumption at$\alpha$ = 0.05, the observed F value is _______.
A)1.78
B)3.79
C)-3.79
D)3.18
E)1.33

Question

Quizplus · Accepted Answer

The observed F value is calculated by dividing the variance of the group with the larger variance by the variance of the group with the smaller variance. The variance is the square of the standard deviation, so for the old diet, the variance is $2^2 = 4$, and for the new diet, the variance is $1.5^2 = 2.25$. Thus, the observed F value is $4 / 2.25 = 1.78$.

A Researcher Believes a New Diet Should Improve Weight Gain α\alphaα

A Researcher Believes a New Diet Should Improve Weight Gain $\alpha$