Writing hypotheses to test the difference of means

An exercise scientist wanted to test the effectiveness of a new program designed to increase the flexibility of senior citizens. They recruited participants and rated their flexibility according to a standard scale before starting the program. The participants all went through the program and had their flexibility rated again after a month.

The scientist wants to test if the flexibility ratings are significantly higher after a month of the program. Assume that these participants can be considered a representative sample and that all other necessary conditions for inference were met.

Which of these is the most appropriate test and alternative hypothesis?

(Choice A)
Paired $t$ ‍ test with $H_{a} : μ_{after - before} > 0$ ‍
(Choice B)
Paired $t$ ‍ test with $H_{a} : μ_{after - before} \neq 0$ ‍
(Choice C)
Two-sample $t$ ‍ test with $H_{a} : μ_{before} > μ_{after}$ ‍
(Choice D)
Two-sample $t$ ‍ test with $H_{a} : μ_{before} \neq μ_{after}$ ‍
(Choice E)
Two-sample $t$ ‍ test with $H_{a} : μ_{before} < μ_{after}$ ‍

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 11

Problem