Question

A certain diet plan claims that subjects lose an average of 20 pounds in 6 months on their plan. A dietitian wishes to test this claim and recruits 15 people to participate in an experiment. Their weight is measured before and after the 6-month period. Which is the appropriate test statistic to test the diet company's claim?

a. two-sample Z test

b. two-sample T test

c. paired T test

Answer 1

`t = (\bar d -\Delta)/((s_d)/(√(n)))`

And the best option for this case is:

c. paired T test

Explanation:

For this case we want to check if the subjects with a certain diet plan lose an average of 20 pounds in 6 months on their plan.

They select a sample size of n =15. and we will have measures before and after. Let's say that x represent the values before and y represent the values after and for this case we can define the difference like this:

`d = y_i - x_i , i =1,2,...,n`

We want to test the following system of hypothesis:

Null hypothesis:
`d \leq -20`

Alternative hypothesis:
`d >-20`

And for this case the correct statistic would be:

`t = (\bar d -\Delta)/((s_d)/(√(n)))`

And the best option for this case is:

c. paired T test