concept of one-tailed hypothesis testing 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?

An example, where the alternative hypothesis is _not_ $H_A: \theta \
eq \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:

$H_0:\theta=0.1$

$H_A:\theta \geq 0.1$