# Interpretation of null and alternative hypotheses

The way I interpreted this question was that $H_0: \mu \ge 10, H_a: \mu < 10$. But the answer for this question set up a hypothesis of $H_0: \mu = 10,H_a: \mu>10$. Shouldn't it be the first way?

If "the claim" is "that it takes at least 10 years", and you want to test this, then that is your alternative hypothesis. The null hypothesis negates the alternative. Thus:
$$H_0: \mu\le10 \\ H_a: \mu>10$$ A way to think about these things is that the alternative hypothesis is what the researcher really believes, but she is worried that there is someone who is so skeptical that they won't believe her unless the evidence against the null is sufficiently strong.

I am bit confused with gung's interpretation. Please correct me if I am wrong.

Since the claim is that it takes 'at least 10 years', then we should state this claim as mu>=10, and the other hypothesis should be the complementary of this one, so it is mu<10.

To my understanding, the claim of 'mu>=10' has to be the null hypothesis because it contains '=' sign. This is important when we calculate the maximum value of restricted likelihood, because the maximum value will lie on the boundary of the support, so the boundary value (10 in this case), needs to be contained in the support. Thus we need the '=' sign in the null hypothesis.

So I tend to agree with user28884's original interpretation.

Ho : mu > = 10 Ha: mu < 10

Descriptive Statistics Column 1

Sample Size, n: 10 Mean: 11.72 Variance, s^2: 8.179556 St Dev, s: 2.859992

test statistics , t = (11.72 - 10)/(2.86/sqrt(10)) = 1.9017

critical t (9, 0.05)= - 1.833.

hence, computed t (1.9017) > critical t (-1.833) .

Fail to reject Ho.

http://tutorteddy.com/site/free_statistics_help.php

• Can you summarize in plain English the above procedure? It would certainly be useful for the OP to get better than a series of formulae and results.
– chl
Aug 10, 2013 at 8:34
• (-1) The OP apparently seeks guidance in terms of stating a NHST, not numerical results (without further interpretation of them). Also, there's no need to sign your post with a link to a specific website, which might be seen as some sort of advertising (it is frowned upon on SE sites, or there should be proper disclosure).
– chl
Aug 12, 2013 at 21:01