Please find a the probability associated with the mean of 75

Please find:

a- the probability associated with the mean of 75 is p=0.05. Can we reject the null hypothesis?

b- if the null hypothesis is a correct statement, what is the probability that the researcher will make the correct decision not to reject the null hypothesis?

Solution

a)As the p-value is .05 which is equal to the significance level of .05 therefore we should accept the null hypothesis as the hypothesis lies in the acceptance region

b)Probability that the researcher will make the correct decision of not rejecting the null hypothesis =1-.05 =.95