A test of $H _ { 0 } : \mu =$ 45 versus $H _ { 1 } : \mu

Question

A test of $H _ { 0 } : \mu =$ 45 versus $H _ { 1 } : \mu < 45$  is performed using a significance level of $\alpha$ =0.01. The value of the test statistic is z=-2.24.
If the true value of $\mu$ is 45 , does the conclusion result in a Type I error, a Type II error, or a correct decision?
A) Type I error
B) Correct decision
C) Type II error

Quizplus · Accepted Answer

A Type I error occurs when the null hypothesis is true but is incorrectly rejected. Since the test statistic z = -2.24 is not less than the critical value for $\alpha$ = 0.01 (approximately -2.33 for a one-tailed test), we do not reject $H_0$. Therefore, we make a correct decision as we do not reject the true null hypothesis.

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