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