Type I probabilty is used extensively in hypothesis testing
That means that the probability of rejecting the null hypothesis, when μ = 108 is 0.3722 as calculated here:
Probability and hypothesis testing problems  BrainMass
Definition. The power of a hypothesis test is the probability of making the correct decision if the alternative hypothesis is true. That is, the power of a hypothesis test is the probability of rejecting the null hypothesis H_{0} when the alternative hypothesis H_{A} is the hypothesis that is true.
In hypothesis testing, probability models are used to control the proportion of times a researcher claims to have found effects when in fact the results were due to chance or haphazard circumstances. Because the science as a whole is able to participate in the long run, these models have been successfully applied with the result that only a small proportion of published research is the result of chance, coincidence, or haphazard events.
probability  Null Hypothesis  Mathematics Stack …
Incidentally, we can always check our work! Conducting the survey and subsequent hypothesis test as described above, the probability of committing a Type I error is:
Area under theoretical models of distributions is the method that classical hypothesis testing employs to estimate probabilities. A major part of an intermediate course in mathematical statistics is the theoretical justification of the models that are used in hypothesis testing.
Hypothesis Testing and Probability Theory
(2) We can see that the probability of a Type I error is α = K(100) = 0.05, that is, the probability of rejecting the null hypothesis when the null hypothesis is true is 0.05.
Solution. Setting α, the probability of committing a Type I error, to 0.01, implies that we should reject the null hypothesis when the test statistic Z ≥ 2.326, or equivalently, when the observed sample mean is 109.304 or greater:
Probability hypothesis density filter for radar …

Probability of Hypothesis – ecyY
the probability that the observed experimental difference is due to chance given the null hypothesis.

Probability, correlation, null or alternative hypothesis, ..
assume that the alternative hypothesis is Ha: the probability of a head is 0.7.

as that is the probability that the original hypothesis is rejected.
The solution provides step by step method for the calculation of problems from probability and hypothesis testing
Null Hypothesis (1 of 4)  David Lane
Solution. Setting α, the probability of committing a Type I error, to 0.05, implies that we should reject the null hypothesis when the test statistic Z ≥ 1.645, or equivalently, when the observed sample mean is 106.58 or greater:
The null hypothesis is an hypothesis about a population parameter
Now, that implies that the power, that is, the probability of rejecting the null hypothesis, when μ = 108 is 0.6406 as calculated here (recalling that Φ(z) is standard notation for the cumulative distribution function of the standard normal random variable):
Onesample z and t significance tests
Solution. Because we are setting α, the probability of committing a Type I error, to 0.05, we again reject the null hypothesis when the test statistic Z ≥ 1.645, or equivalently, when the observed sample mean is 106.58 or greater. That means that the probability of rejecting the null hypothesis, when μ = 112 is 0.9131 as calculated here:
Hypothesis Representation  Stanford University  Coursera
If, unknown to the engineer, the true population mean were μ = 173, what is the probability that the engineer makes the correct decision by rejecting the null hypothesis in favor of the alternative hypothesis?
Division of Information Technology
In summary, we have determined that we now have a 91.31% chance of rejecting the null hypothesis H_{0}: μ = 100 in favor of the alternative hypothesis H_{A}: μ > 100 if the true unknown population mean is in reality μ = 112. Hmm.... it should make sense that the probability of rejecting the null hypothesis is larger for values of the mean, such as 112, that are far away from the assumed mean under the null hypothesis.
Statistical hypothesis testing  Wikipedia
Solution. Again, because we are setting α, the probability of committing a Type I error, to 0.05, we reject the null hypothesis when the test statistic Z ≥ 1.645, or equivalently, when the observed sample mean is 106.58 or greater. That means that the probability of rejecting the null hypothesis, when μ = 116 is 0.9909 as calculated here: