A test of $H _ { 0 } : \mu = 59$ versus $H _ { 1 } : \mu

Question

A test of $H _ { 0 } : \mu = 59$ versus $H _ { 1 } : \mu < 59$ is performed using a significance level of $\alpha = 0.05$. The value of the test statistic is $z = - 1.80$.
If the true value of $\mu$ is 59 , does the conclusion result in a Type I error, a Type II error, or correct decision?
A) Correct decision
B) Type II error
C) Type I error

Quizplus · Accepted Answer

A Type I error occurs when the null hypothesis is rejected when it is actually true. Since the test is looking for evidence that $\mu < 59$, and the null hypothesis $H_0: \mu = 59$ is true, rejecting $H_0$ based on the test statistic would result in a Type I error.

A Test Of H0:μ=59H _ { 0 } : \mu = 59H0​:μ=59

A Test Of $H _ { 0 } : \mu = 59$