i. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt that the null hypothesis is true. ii. A test statistic is a value determined from sample information collected to test the null hypothesis.
iii. The region or area of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.
A) (ii) and (iii) are correct statements but not (i).
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

Quizplus · Accepted Answer

Failing to reject the null hypothesis does not prove it true beyond doubt; it simply means there's not enough evidence against it. A test statistic is indeed calculated from sample data to test the null hypothesis, and the rejection region defines values that would be unlikely if the null hypothesis were true, indicating a significant result.

I If We Do Not Reject the Null Hypothesis Based