Question

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.

Diet 1 3.4 10.9 2.8 7.8 0.9 5.2 2.5 10.5 7.1 7.5
Diet 2 11.9 13.1 11.6 6.8 6.8 8.8 12.5 8.6 17.5 10.3
Carry out an appropriate test using a significance level of 0.10.

Answer 1

WE reject the Null and conclude that one of the drug is more effective than the other.

Explanation:

Given :

Diet 1 3.4 10.9 2.8 7.8 0.9 5.2 2.5 10.5 7.1 7.5

Diet 2 11.9 13.1 11.6 6.8 6.8 8.8 12.5 8.6 17.5 10.3

This is a matched pair sample :

The hypothesis :

H0 : μd = 0

H1 : μd ≠ 0

Hence, we intun the difference between the two groups of value :

Difference, d = -8.9,-2.2,-8.8,1,-5.9,-3.6,-10,1.9,-10.4,-2.8

The test statistic :

dbar ÷ (Sd/√n)

dbar = mean of difference = Σd / n = - 49.7 / 10 = - 4.97

Standard deviation of difference, Sd = 4.51

Test statistic :

-4.97 ÷ (4.51/√10)

Test statistic = - 3.485

The sample size, n = 10

df = n - 1 ; 10 - 1 = 9

Critical value (0.10, 9) = 1.833

If Test statistic > |Critical value |

Since 3.486 > 1.833 ; WE reject the Null and conclude that one of the drug is more effective than the other