In a hypothesis test, the significance level α (alpha)represents the threshold for how unlikely sample data has to be,assuming the null hypothesis, in order for us to reject the nullhypothesis. Often alpha is taken to be 0.05, or 1/20, which meansthat even if the null hypothesis is true, there is a 1/20chance that we will reject it because our sample data happens tohave a P-value less than 0.05.
We want to study the heights of students. Our null hypothesisH_0 is that the average height is 67 inches, and the alternatehypothesis is that the average height is not 67 inches. We usesignificance level 0.05.
A) Suppose we run a hypothesis test. In the test, the data had aP-value less than 0.05. What should the conclusion of the testbe?
B) Suppose we run 20 hypothesis tests on this, each with adifferent sample. In nineteen of these tests, our sample data had aP-value greater than 0.05. In one test, the data had a P-value lessthan 0.05. Does this evidence, as a whole, support the hypothesisthat the average height is 67 inches? Explain your thinking.
