Question

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II.The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7. Identify the type 2 error for the test.

Answer 1

We know that type II error is failing to reject the null hypothesis that is actually false. This means that we didn't reject the false null hypothesis.

In this case, we have to test the claim that the test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7

Null hypothesis for this situation is "test scores of the seventh-graders at his school are equal to the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7"

We assume the test scores to be equal for both the schools.

Type II error is failing to reject the false null hypothesis, So type II error in this case will be the conclusion that "the test scores of the seventh-graders at his school are equal to the test scores of the seventh-graders at a neighboring school, even when the test scores are not equal for both school's seventh graders".