Question

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. The principal of a school claims that the percentage of students at his school that come from single- parent homes is 11 %. Identify the type II error for the test.

Answer 1

Type I error: Concluded that p ≠ 11% when it is 11%.

Type II error: Concluded that p = 11% when it is not 11%.

Explanation:

A type I error is the rejection of the null hypothesis (H₀) when indeed the null hypothesis is true. It is symbolized by α.

A type II error is failing to discard the null hypothesis when indeed the null hypothesis is false. It is symbolized by β.

In this case a principal of a school claims that the percentage of students at his school that come from single-parent homes is 11%.

The hypothesis to test this claim is:

H₀: The proportion of students at the school that come from single-parent homes is 11%, i.e. p = 0.11.

Hₐ: The proportion of students at the school that come from single-parent homes is not 11%, i.e. p ≠ 0.11.

• The type I error will be committed when it is concluded that the proportion of students at the school that come from single-parent homes is not 11% when in fact it is 11%.
• The type II error will be committed when it is concluded that the proportion of students at the school that come from single-parent homes is 11% when it is not.