91 A powder diet is tested on 49 people and a liquid diet is

91. A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds.

Solution

Let mu1 be the mean for liquid diet group

Let mu2 be the mean for power diet

The test hypothesis:

Ho: mu1=mu2 (i.e. null hypothesis)

Ha: mu1>mu2 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(45-42)/sqrt(12^2/49+14^2/36)

=1.04

It is a right-tailed test.

Assume that the significant level a=0.05

The critical value is Z(0.05) = 1.645 (from standard normal table)

The rejection region is if Z>1.645, we reject the null hypothesis.

Since Z=1.04 is less than 1.646, we do not reject the null hypothesis.

So we can not conclude that the liquid diet yields a higher mean weight loss than the power diet