Question

A test of H0: μ = 60 versus H1: μ ≠ 60 is performed using a significance level of 0.01. The P-value is 0.033. If the true value of μ is 53, does the conclusion result in a Type I error, a Type II error, or a correct decision?

Answer 1

Solution :

The null and alternative hypotheses are as follows :

H0: μ = 60 versus H1: μ ≠ 60

p-value = 0.033

Significance level = 0.01

Since, p-value is greater than the significance level of 0.01, therefore we shall be fail to reject the null hypothesis (H​​​​​​0).

True value of μ is 53.

Type I and type II error are defined as follows :

Type I error : The error committed by rejecting the null hypothesis, when actually the null hypothesis is true, is known as type I error.

Type II error : The error committed by not rejecting the null hypothesis, when actually the null hypothesis is false, is known as type II error.

Here, we are not rejecting the null hypothesis that μ = 60, when actually the null hypothesis is false (i.e. μ = 53). It means we are committing a type II error.

Hence, the conclusion would result in a type II error.