Researchers were interested in comparing the long-term psychological effects of being on a high-carbohydrate, low-fat (LF) diet versus a high-fat, low-carbohydrate (LC) diet. A total of106 overweightand obese participants were randomly assigned to one of these two energy-restricted diets. At52 weeks,32 LCdieters and33 LFdieters remained. Mood was assessed using a total mood disturbance score (TMDS), where a lower score is associated with a less negative mood. A summary of these results follows.

Group n x-bar s

LC 32 47.2 28.2

LF 33 19.4 25.7

(a) Is there a difference in the TMDS at Week 52? Test the null hypothesis that the dieters' average mood in the two groups is the same. Use a significance level of 0.05.

State the null and alternate hypothesis.

Report the test statistic with the degrees of freedom and theP-value. (Round your value fortto three decimal places, your degrees of freedom to the nearest whole number, and yourP-value to four decimal places.)

t=

df=

p-value=

State the conclusion.