Bob is conducting a two tailed hypothesis test. He observes a T-stat of -1.38 which was based on a sample of size 20 where the population mean = 0. Bob chose a 5% level of significance - he should:
To cut to the chase, bob should fail to reject, but the explanation for the null and alternative hypothesis left me a bit confused. There is no clear explanation as to what Bob thinks the outcome will be, but many similar problems (where the person doing the observing noted that, say, mean >1) had the alternative hypothesis as m>1 while the null hypothesis would be n<=1. I had:
Ha: M§ = 0
Ho: M§ =/ 0
The explanation in the book is saying that the null hypothesis is the population mean is not significantly different from zero. Can someone explain why?
There are two important points about the null hypothesis:
- It’s the hypothesis you would like to reject
- It always includes the equal sign
For the first point, what you choose as the null hypothesis can depend on your point of view. If one of your colleagues claims that the average monthly return on the fund he manages exceeds 1%, then you’ll probably choose H0: μ ≤ 1%, Ha: μ > 1%; i.e., you probably want to show that he’s correct by rejecting a null hypothesis that says he’s wrong. However, if a competitor made the same claim about his fund’s returns, you’d likely choose H0: μ ≥ 1%, Ha: μ < 1%; i.e., you probably want to show that he’s wrong by rejecting a null hypothesis that says he’s right.
The second point is simply that the formulation of the null and alternative hypothesis will take one of three forms (where I’m using the variable μ only as an example; the hypotheses can be about any parameter):
- H0: μ ≤ μ0, Ha: μ > μ0
- H0: μ ≥ μ0, Ha: μ < μ0
- H0: μ = μ0, Ha: μ ≠ μ0
As for Bob: I have no idea what he wants to conclude. Take comfort that on the real exam they will make it clear what Bob wants to conclude; that’ll be Bob’s _ alternative _ hypothesis.