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.

Group of answer choices

Answer 1

Solution:

Claim : percentage is 11%

So , the null and alternative hypothesis are

H₀ : p = 11% vs H₁: p 11%

We know that

Type I error : Reject the null hypothesis when the null hypothesis is true.

Type II error : Fail to reject the null hypothesis , when in fact , the the null hypothesis is NOT true.

So , for given problem ,

Type II error is

to conclude that  the percentage of students at his school that come from single-parent homes is 11%(i.e. not different from 11%) , when in fact , the percentage is actually different from 11%.