William Adams wants to test whether the mean monthly returns over the last five years are the same for two stocks. If he assumes that the returns distributions are normal and have equal variances, the type of test and test statistic are best described as:

A. paired comparisons test, t-statistic.

B. paired comparisons test, F-statistic.

C. difference in means test, t-statistic.

The answer is A. But after I read the explantion, I still don’t understand why paired comparison test is used because I thought it was difference in means test (answer C). Can anyone help me

You’re correct; they blew it.

We have to look at the null hypothesis.

Answer A means that the null hypothesis is

mean(stock A) = mean(stock B)

while answer C means

mean(stock A) - mean(stock B) = some_number

mathematically A and C are equivalent if some_number is 0.

the problem should have been more specific. as written, both answer should work.

for option C, all we have to do is set some_number to 0.

edit:

answer C would be incorrect for any value of some_number other than zero, while answer A is always correct. Because option C can be incorrect depending on the value of some_number, the solution chooses A as the best answer.

Someone has already used something like this, so how is this work?

Thank you for your explanation