A test of $H _ { 0 } : \mu = 55 \text { versus } H _ { 1 } : \mu

Question

A test of $H _ { 0 } : \mu = 55 \text { versus } H _ { 1 } : \mu < 55$ is performed using a significance level of $\alpha = 0.01$ The value of the test statistic is $z = - 2.53 . \text { Is } H _ { 0 }$ rejected?
A) Yes
B) No
C) It cannot be determined.

Quizplus · Accepted Answer

Given the significance level $\alpha = 0.01$ and the test statistic $z = -2.53$, we compare the test statistic to the critical value for a one-tailed z-test at $\alpha = 0.01$, which is approximately -2.33. Since -2.53 is less than -2.33, we reject $H_0$.

A Test Of H0:μ=55 versus H1:μ<55H _ { 0 } : \mu = 55 \text { versus } H _ { 1 } : \mu < 55H0​:μ=55 versus H1​:μ<55

A Test Of $H _ { 0 } : \mu = 55 \text { versus } H _ { 1 } : \mu < 55$