Test the claim about the population mean $\mu$ at the level of significance α. Assume the population is normally distributed. Claim: $\mu 28 ; \alpha = 0.05 ; \sigma = 1.2$
Sample statistics: $\bar { x } = 28.3 , n = 50$
A)Reject $\mathrm { H } _ { 0 }$ . There is enough evidence at the 5% level of significance to support the claim.
B)Fail to reject $\mathrm { H } _ { 0 } \text {. }$ There is not enough evidence at the 5% level of significance to support the claim.
C)Not enough information to decide.

Question

Test the claim about the population mean $\mu$ at the level of significance α. Assume the population is normally distributed. Claim: $\mu > 28 ; \alpha = 0.05 ; \sigma = 1.2$
Sample statistics: $\bar { x } = 28.3 , n = 50$
A)Reject $\mathrm { H } _ { 0 }$ . There is enough evidence at the 5% level of significance to support the claim.
B)Fail to reject $\mathrm { H } _ { 0 } \text {. }$ There is not enough evidence at the 5% level of significance to support the claim.
C)Not enough information to decide.

Quizplus · Accepted Answer

To test the claim, we use the formula for the z-test since $\sigma$ is known: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$. Plugging in the given values: $z = \frac{28.3 - 28}{1.2/\sqrt{50}}$, we find that z is greater than the critical value for $\alpha = 0.05$ in a right-tailed test. Therefore, we reject $H_0$ and conclude there is enough evidence to support the claim that $\mu > 28$.

Test the Claim About the Population Mean μ\muμ At the Level of Significance α

Test the Claim About the Population Mean $\mu$ At the Level of Significance α