How to determine Two-tailed or One-tailed test?

Question

For example while testing difference of two means $\mu_1-\mu_2$ as the numerator in the test statistic, is this left-tailed or right tailed? What if I take $\mu_2-\mu_1$ in the numerator? Will the left right be swapped? Another question is suppose if the $z$ value is 6.58 for a left tailed test at 1% significance level, this should be accepted right? Since the value is to the right of critical value.

Answer 1

the understanding if the text is one or two tails depends mostly on the context:

Example 1:

An electronic device has a mean lifetime of 10 hours. After some improvements, the factory delcares that the new device has a longer lifetime. To prove this hypothesis, 4 items are tested with the following results:

$\{10.1;9.8;9.4;11.5\}$

The sample mean is $10.2>10$

This is a One tail test, as you must understand if actually $10.2>10$ or the difference is due only to the randomness

Example 2:

To verify that a coin is fair, the coin is tossed 10 times giving the following results

$\{T,T,H,T,T,H,T,H,T,T\}$

this is a Two tails Test.