the null hypothesis is not rejected when it is false c.

The p-value, which directly depends on a given sample attempts to provide a measure of the strength of the results of a test for the null hypothesis, in contrast to a simple reject or do not reject in the classical approach to the test of hypotheses.

Power = (1 - eta) = the probability of correctly rejecting a false null hypothesis.
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For example, we accept the alternative hypothesis H and reject the null H, if an event is observed which is at least a-times greater under H than under H.

the null hypothesis is probably wrong b.

So we should reject the null hypothesis when the observed sample mean is 172.961 or greater:
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Understand that the distribution of p-values under null hypothesis H is uniform, and thus does not depend on a particular form of the statistical test.

An Application: Suppose we wish to test the null hypothesis


This statistic is then used for testing the above null hypothesis.

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Hypothesis testing - Handbook of Biological Statistics

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Null and Alternative Hypothesis | Real Statistics Using …

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Statistical hypothesis testing - Wikipedia

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Probability of rejecting the null hypothesis - Experts Mind

There are many statistical procedures for determining, on the basis of a sample, whether the true population characteristic belongs to the set of values in the hypothesis or the alternative.