Question

Given H0: μ ≥ 18 and H1: μ < 18, we would commit a Type I error if we

a) conclude μ ≤ 18 when μ > 18.
b) conclude that μ ≥ 18 when the truth is that μ < 18.
c) fail to reject μ ≥ 18 when the truth is that μ < 18.
d) conclude that μ < 18 when the truth is that μ ≥ 18.

Answer 1

A Type I error would occur if we conclude that μ < 18 when the truth is that μ ≥ 18, which corresponds to option d).

Step-by-step explanation:

The given hypotheses are H0: μ ≥ 18 and H1: μ < 18. A Type I error occurs when we incorrectly reject the null hypothesis when it is actually true.

In this context, it means we would make a Type I error if we concluded that μ < 18 when in reality μ is greater than or equal to 18.

So the correct answer is: d) conclude that μ < 18 when the truth is that μ ≥ 18.

A Type II error, on the other hand, occurs when we fail to reject the null hypothesis when it is actually false.

So among the choices given, a Type II error isn't described.