Which of the following is not correct?

A. The rejection region is controlled by the alpha level and the alternate hypothesis.
B. The p-value measures the probability that the null hypothesis is true.
C. The probability of a Type I error is controlled by the selection of the alpha level.
D. The probability of a Type II error is controlled by the sample size.
E. The power of a test depends upon the sample size and the distance between the null and alternate hypothesis.

Since the probability of a Type II error is equal to beta, I would say D is not correct.

the probability of type ii error decreases when the sample data increases

To determine which of the options is not correct, we need to understand the concepts mentioned in each statement and compare them to evaluate their accuracy.

A. The rejection region is controlled by the alpha level and the alternate hypothesis.
This statement is true. The rejection region is the range of values that, if the test statistic falls within it, leads to rejecting the null hypothesis. The alpha level determines the extent to which the null hypothesis is rejected, and the alternate hypothesis specifies the range of values for which the null hypothesis is rejected.

B. The p-value measures the probability that the null hypothesis is true.
This statement is not correct. The p-value is the probability of obtaining the observed data or more extreme values assuming that the null hypothesis is true. It measures the strength of the evidence against the null hypothesis but does not directly measure the probability that the null hypothesis is true.

C. The probability of a Type I error is controlled by the selection of the alpha level.
This statement is true. The Type I error refers to rejecting the null hypothesis when it is true. The alpha level determines the threshold for rejecting the null hypothesis, and selecting a smaller alpha level reduces the probability of committing a Type I error.

D. The probability of a Type II error is controlled by the sample size.
This statement is not correct. The probability of a Type II error refers to failing to reject the null hypothesis when it is false. The sample size affects the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false. A larger sample size generally increases the power and reduces the probability of a Type II error.

E. The power of a test depends upon the sample size and the distance between the null and alternate hypothesis.
This statement is true. The power of a test is influenced by the sample size, as a larger sample size provides more information and increases the ability to detect a true difference. The power also depends on the distance or effect size between the null and alternate hypothesis. A larger effect size makes it easier to detect a true difference and increases the power of the test.

Therefore, the statement that is not correct is:
B. The p-value measures the probability that the null hypothesis is true.