Test the claim about the population mean μ at the level of significance α $\alpha$ Assume the population is normally distributed. Claim: $\mu \neq 35 ; \alpha = 0.05 ; \sigma = 2.7$
Sample statistics: $\overline { \mathrm { x } } = 34.1 , \mathrm { n } = 35$
A)Reject $\mathrm { H } _ { 0 } .$ There is enough evidence at the 5% level of significance to support the claim.
B)Fail to reject $\mathrm { H } _ { 0 }$ There is not enough evidence at the 5% level of significance to support the claim.
C)Not enough information to decide.

Question

Quizplus · Accepted Answer

The test statistic is calculated as $ z = \frac{\overline{x} - \mu}{\sigma/\sqrt{n}} = \frac{34.1 - 35}{2.7/\sqrt{35}} \approx -2.08 $. The critical z-values for a two-tailed test at $\alpha = 0.05$ are approximately $\pm 1.96$. Since $-2.08$ is outside the range $-1.96$ to $1.96$, we reject $H_0$.

Test the Claim About the Population Mean μ at the Level