A test of $H _ { 0 } : \mu = 61$ versus $H _ { 1 } : \mu 61$ is performed using a significance level of $\alpha = 0.05$. The $P$-value is $0.101$. If the true value of $\mu$ is 61 , does the conclusion result in a Type I error, a Type II error, or a correct decision?
A) Type I error
B) Type II error
C) Correct decision

Question

A test of $H _ { 0 } : \mu = 61$ versus $H _ { 1 } : \mu > 61$ is performed using a significance level of $\alpha = 0.05$. The $P$-value is $0.101$. If the true value of $\mu$ is 61 , does the conclusion result in a Type I error, a Type II error, or a correct decision?
A) Type I error
B) Type II error
C) Correct decision

Quizplus · Accepted Answer

Since the P-value (0.101) is greater than the chosen significance level (0.05), we fail to reject the null hypothesis. This means we do not have sufficient evidence to conclude that the population mean is greater than 61. Since the true value of μ is 61, our decision is correct. Therefore, the answer is C.

A Test Of H0:μ=61H _ { 0 } : \mu = 61H0​:μ=61

A Test Of $H _ { 0 } : \mu = 61$