Test the claim about the difference between two population means $\mu_1$ and $\mu_2$ at the level of significance $\alpha$. Assume the samples are random and independent, and the populations are normally distributed.
Claim: $\mu_1 = \mu_2$; $\alpha = 0.01$
Population parameters: $\sigma_1 = 3.2$, $\sigma_2 = 1.7$
Sample statistics: $x_1 = 15$, $n_1 = 29$, $x_2 = 13$, $n_2 = 26$
Determine the alternative hypothesis.
$H_a: \mu_1 \ne \mu_2$
Determine the standardized test statistic.
$z = 2.47$ (Round to two decimal places as needed.)
Determine the P-value.
P-value = 0.014 (Round to three decimal places as needed.)
What is the proper decision?
A. Reject $H_0$. There is not enough evidence at the 1% level of significance to reject the claim.
B. Fail to reject $H_0$. There is enough evidence at the 1% level of significance to reject the claim.
C. Fail to reject $H_0$. There is not enough evidence at the 1% level of significance to reject the claim.
D. Reject $H_0$. There is enough evidence at the 1% level of significance to reject the claim.
