Alternate and Null Hypothesis in 1 vs 2 tailed hypothesis

CFA Level I Quant
#1

I understand that the alternative hypothesis is supposed to be what we are testing for…

“The researchers want to know if the means is grreater than 100…” = Ha = u>100.

But is this rule flipped for a two tailed test? I keep finding questions like this one…

Mike is testing whether a population’s mean equals 25. He computes a t‐stat of 1.71 based on a sample of 20 observations, assuming that the population is normally distributed. At the 10% level of significance, Mike should most likely: Reject the null hypothesis, and conclude that the population mean is not significantly different from 25. Reject the null hypothesis, and conclude that the population mean is significantly different from 25. Fail to reject the null hypothesis that the population mean equals 25. Solution:

H0: μ = 25; Ha: μ ≠ 25

This is a two‐tailed test. At the 10% level of significance, the critical t‐values for a two‐tailed test given 19 degrees of freedom are ‐1.7291 and +1.7291.

Why would Ha be u(/=) 25??? Thanks for any help.

#2

We’re told that the null hypothesis always has the equal sign, so, based on that rule, you haven’t any choice.

What the first sentence should say is that Mike is testing whether a population’s mean equals 25 _ or not _. Then you wouldn’t be (mis)led to believe that the mean equaling 25 is the alternative hypothesis.

#3

awesome, thanks bill

#4

You’re quite welcome.