Hello, please don\'t use software including Excel when posting the solution. Tha
ID: 3217933 • Letter: H
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Hello, please don't use software including Excel when posting the solution. Thank you!
Two different weight loss programs are being compared to determine their effectiveness. Ten men were assigned to each program (that is, a total of 20 men altogether). Their weight losses (in lbs), after a period of time, are recorded below. We are interested in determining which, if any, of the diets is more effective in terms of average weight loss. Assume weight loss for each diet to be normally distributed. Carry out an appropriate test using a significance level of 0.10.Explanation / Answer
We do a two sample t-test as below and calculate the p-value from t-tables.
Difference Scores Calculations
Treatment 1
N1: 10
df1 = N - 1 = 10 - 1 = 9
M1: 5.86
SS1: 106.66
s21 = SS1/(N - 1) = 106.66/(10-1) = 11.85
Treatment 2
N2: 10
df2 = N - 1 = 10 - 1 = 9
M2: 10.79
SS2: 96.01
s22 = SS2/(N - 1) = 96.01/(10-1) = 10.67
T-value Calculation
s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2+ df2)) * s22) = ((9/18) * 11.85) + ((9/18) * 10.67) = 11.26
s2M1 = s2p/N1 = 11.26/10 = 1.13
s2M2 = s2p/N2 = 11.26/10 = 1.13
t = (M1 - M2)/(s2M1 + s2M2) = -4.93/2.25 = -3.29
The t-value is -3.28526. The p-value is .004113. The result is significant at p < .10.
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