A test of $H _ { 0 } : \mu = 65$ versus $H _ { 1 } : \mu

Question

A test of $H _ { 0 } : \mu = 65$ versus $H _ { 1 } : \mu < 65$ is performed using a significance level of $\alpha = 0.05$. The $P$-value is $0.055$.
If the true value of $\mu$ is 65 , does the conclusion result in a Type I error, a Type II error, or correct decision?
A) Type II error
B) Correct decision
C) Type I error

Quizplus · Accepted Answer

Since the $P$-value (0.055) is greater than the significance level ($\alpha = 0.05$), we fail to reject $H_0$. Given that the true value of $\mu$ is indeed 65, not rejecting $H_0$ is the correct decision, not an error.

A Test Of H0:μ=65H _ { 0 } : \mu = 65H0​:μ=65

A Test Of $H _ { 0 } : \mu = 65$