Question

Assume that a hypothesis test to support the given claim will be conducted. Identify the type I or type II error for the test. The principal of a middle school claims that the standard deviation of the test scores of the seventh-graders at his school is less than 14.7. Identify the type I error for the test.

1) Rejecting the null hypothesis when it is true
2) Failing to reject the null hypothesis when it is false
3) Accepting the null hypothesis when it is true
4) Failing to accept the null hypothesis when it is false

Answer 1

A Type I error in the context of the principal's claim about test scores would occur if the null hypothesis is rejected when it is actually true, which corresponds to option 1) Rejecting the null hypothesis when it is true.

Step-by-step explanation:

When conducting a hypothesis test, committing a Type I error or a Type II error affects the integrity of the test's conclusions. A Type I error occurs when the null hypothesis is incorrectly rejected. Specifically, for the middle school principal's claim, a Type I error would result from rejecting the null hypothesis that the standard deviation of seventh-graders' test scores is at least 14.7 when it is actually true.

The correct answer for identifying the Type I error is: 1) Rejecting the null hypothesis when it is true.