A test of $H _ { 0 } : \mu = 53$ versus $H _ { 1 } : \mu

Question

A test of $H _ { 0 } : \mu = 53$ versus $H _ { 1 } : \mu < 53$ is performed using a significance level of $\alpha = 0.01$. The $P$-value is $0.124$.
If the true value of $\mu$ is 49 , does the conclusion result in a Type I error, a Type II error, or correct decision?
A) Type II error
B) Type I error
C) Correct decision

Quizplus · Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. Since the true value of $\mu$ is 49, which is less than 53, the null hypothesis $H_0: \mu = 53$ should be rejected in favor of $H_1: \mu < 53$. However, because the $P$-value of 0.124 is greater than the significance level of 0.01, the test fails to reject $H_0$, leading to a Type II error.

A Test Of H0:μ=53H _ { 0 } : \mu = 53H0​:μ=53

A Test Of $H _ { 0 } : \mu = 53$