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

Respuesta :

Answer:

[tex] t = \frac{\bar d -\Delta}{\frac{s_d}{\sqrt{n}}}[/tex]

And the best option for this case is:

c. paired T test

Step-by-step 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:

[tex] d = y_i - x_i , i =1,2,...,n[/tex]

We want to test the following system of hypothesis:

Null hypothesis: [tex] d \leq -20 [/tex]

Alternative hypothesis: [tex] d >-20 [/tex]

And for this case the correct statistic would be:

[tex] t = \frac{\bar d -\Delta}{\frac{s_d}{\sqrt{n}}}[/tex]

And the best option for this case is:

c. paired T test