Question

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: $sigma_1 = 3.3$, $sigma_2 = 1.5$
sample statistics: $overline{x}_1 = 18$, $n_1 = 20$, $overline{x}_2 = 20$, $n_2 = 30$
determine the p - value
p - value = 0.003 (round to three decimal places as needed)
what is the proper decision?
a. reject $h_0$. there is 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 not enough evidence at the 1% level of significance to reject the claim.

Explanation:

Step1: State the decision rule

If \(P - value<\alpha\), reject \(H_0\). Here, \(\alpha = 0.01\) and \(P - value=0.003\).

Step2: Compare \(P - value\) and \(\alpha\)

Since \(0.003<0.01\) (i.e., \(P - value<\alpha\)).

Answer:

A. Reject \(H_0\). There is enough evidence at the \(1\%\) level of significance to reject the claim.