Formulate null and alternative hypotheses


please see the question below:

Their answer is: We test H0: μd* = 0 versus Ha : μd ≠ 0.

Why don’t they use H0: μd* = -0.258 versus Ha : μd ≠ -0.258 instead?

Note the phrase “whether any difference exists”: this means we want to know if the difference is exactly 0 or something else.

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Hi Kaplan93,

It is important to note that the alternative hypothesis is tipically the research hyphotesis. In this case, you want to evaluate if the difference between S&P and Small-Cap stocks mean return is indeed significant, i.e not equal to 0.

So we are not concerned with the reported difference (-0.258), rather we are focused on testing if this difference in fact exists.

Therefore, H0: μd = 0 | Ha: μd ≠ 0

Hope it helps. If not, just let me know. Thank you.