A test of $H _ { 0 } : \mu = 49$ versus $H _ { 1 } : \mu

Question

A test of $H _ { 0 } : \mu = 49$ versus $H _ { 1 } : \mu < 49$ is performed using a significance level of $\alpha = 0.05$. The value of the test statistic is $z = - 1.70$.
If the true value of $\mu$ is 45 does the conclusion result in a Type I error, a Type II error, or ह correct decision?
A) Type II error
B) Correct decision
C) Type I error

Quizplus · Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. Since the true mean ($\mu = 45$) is less than the hypothesized mean ($\mu = 49$), and the test statistic ($z = -1.70$) likely leads to rejecting the null hypothesis (depending on the critical value for $\alpha = 0.05$ in a one-tailed test), this scenario results in a correct decision rather than an error, assuming the critical value is around -1.645 or less negative.

A Test Of H0:μ=49H _ { 0 } : \mu = 49H0​:μ=49

A Test Of $H _ { 0 } : \mu = 49$