Question

A women’s figure salon specializes in weight reduction. A sample of six women were used to see if their program was effective. After the program the average difference (after - before) is weight for the six women was -6.7 lbs. with a standard deviation of 6.59 lbs. Test whether the weight reduction program significantly reduced the women’s weight at the 0.01 level of significance. Based on your results would you recommend this program?

Answer 1

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

H₀: µ_d = 0 versus H_a: µ_d < 0

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

µ_d =0

Dbar = -6.7

S_d = 6.59

n = 6

df = n – 1 = 5

α = 0.01

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (-6.7 - 0)/[6.59/sqrt(6)]

t = -2.4904

The p-value by using t-table is given as below:

P-value = 0.0276

P-value > α = 0.01

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the weight reduction program significantly reduced the women’s weight at the 0.01 level of significance.