i. Two types of possible errors always exist when testing hypotheses-a Type I error, in which the null hypothesis is rejected when it should not have been rejected, and a Type II error in which the null hypothesis is not rejected when it should have been rejected. ii. A test statistic is a value determined from sample information collected to test the null hypothesis.
iii. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt that the null hypothesis is true.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question

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(i) and (ii) are correct and well-established principles of hypothesis testing. However, (iii) is not correct as failing to reject the null hypothesis does not prove that it is true, but rather that there is not enough evidence to reject it. Remember that the null hypothesis is simply a starting point for hypothesis testing and should be rejected only if the evidence strongly suggests that it is false.

I Two Types of Possible Errors Always Exist When Testing