Question

A doctor wishes to determine which of two diets is more effective in reducing weight. A sample of 20 obese adults who are interested in losing weight is randomly divided into groups of 10. After 6 weeks the weight loss of each participant was recorded. The mean for diet 1 is 8 pounds with a standard deviation of 3.23 pounds. The mean for diet 2 is 11 pounds with a standard deviation of 6.78 pounds. Does the data justify the conclusion that the mean weight loss on diet 2 was greater than the mean weight loss on diet 1? a = .05

Answer 1

Solution

Given ,

  = 8 = 11

s₁ = 3.23 s₂ = 6.78

n₁ = 10 n₂ = 10

= 0.05

Use pooled t test and pooled confidence interval for the difference between two population means.

The claim is "the mean weight loss on diet 2 was greater than the mean weight loss on diet 1"

i.e  ₂ >  ₁

i.e  ₁ <  ₂

The hypothesis are

H0:  ₁ =  ₂

Ha : ₁ <  ₂

The test statistic t is given by

t =

where    denotes the pooled variance.

t =   

=

t =  -1.263 is the value of the test statistic.

d.f. = n₁ + n₂ - 2 = 10 + 10 - 2 = 18

< sign in Ha indicates that " Left tailed test"

The Critical value is   =    = -1.734

  t = -1.263 is greater than = -1.734

t = -1.263 falls in "do not reject Ho region" because it is left tailed test.

We fail to reject H0 at 0.05 level and conclude that "the mean weight loss on diet 2 was not significantly greater than the mean weight loss on diet 1"