Question

In a recent medical study, 81 subjects were placed on a low-fat diet. After 12 months, their sample mean weight loss was 2.2 kilograms, with a sample standard deviation of 6.1 kilograms. Construct an appropriate test to conclude if the mean weight loss is greater than 0 at an α = 0.01 significance level.

Answer 1

Solution :

= 0

= 2.2

s = 6.1

n = 81

Df = n -1 = 81 -1 80

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 0

Ha : > 0

Test statistic = t

= ( - ) / s/ n

= (2.2 -0) / 6.1 / 81

= 3.246

p(Z >3.246 ) = 1-P (Z <3.246 ) = 0.0009

P-value = 0.0009

= 0.01  

0.0009< 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that