When we assume that the null hypothesis is true in one-tailed test for mean, we assume that the population mean is equal that value indicated in the hypotheses. Why do we not assume some other value for the population mean also allowable under the null hypothesis?
Asked
Active
Viewed 81 times
1 Answers
1
An example, where the alternative hypothesis is not $H_A: \theta \neq \theta_0 $.
A manufacturer claims, that the proportion of defective items is 10% percent . The customer makes a sample to check this hypothesis .
If the proportion of defective items is smaller than 10%, the customer would not reject the commodity. It is quite the reverse. It would be better for the costumer.
Thus the hypotheses are:
$H_0:\theta=0.1$
$H_A:\theta \geq 0.1$
callculus42
- 30,550
-
This is an example. Is there a general explanation why there is not need to assume smaller population proportion? – TooOldToLearn Nov 24 '14 at 21:18
-
It depends on the problem you are faced with. The problem determine the null hypothesis and the aternative hypothesis. But here you do not assume, that the population proportion is smaller. The customer is only interested, if the population proportion is bigger than 10%. – callculus42 Nov 24 '14 at 21:29
-
Can I conclude that if population proportion is assumed any value other than 10%, the test becomes meaningless? – TooOldToLearn Nov 24 '14 at 21:57
-
Yes. You have only 3 possible hypothesis: $H_0:\theta =\theta_0,H_0:\theta \leq \theta_0,H_0:\theta \geq\theta_0$ – callculus42 Nov 24 '14 at 22:14