Final answer:
In the context of hypothesis testing, the null hypothesis is not always accepted, a Type I error is the incorrect rejection of a true null hypothesis, and the level of significance represents the probability of making a Type I error, not a Type II error.
Step-by-step explanation:
The question relates to the topic of hypothesis testing within the field of statistics, a branch of mathematics. When we consider the statements given, we see that:
- The null hypothesis is not always accepted. It is a statement that is tested, and based on the evidence provided by the data, it may be rejected or not rejected. But there is never an acceptance of the null hypothesis in the sense of proving it to be true.
- A Type I error is indeed the rejection of a true null hypothesis. It represents a false positive, where we mistakenly think that our sample provides enough evidence to reject the null hypothesis when it is actually true.
- The level of significance of a hypothesis test is not the probability of a Type II error, but rather the probability of making a Type I error. It is denoted by the Greek letter alpha (α) and is the threshold we set for deciding when to reject the null hypothesis. The probability of a Type II error is denoted by beta (β).
As a result, the accurate statements about hypothesis testing from the list provided are that a Type I error is the rejection of a true null hypothesis and that the level of significance represents the probability of committing a Type I error (not a Type II error).