Answer
Yes, see explanation.
Work Step by Step
Given $n1=15, \mu1=35270, \sigma1=3256$ and $n2=30, \mu2=29512, \sigma2=1432$
a. State the hypotheses and identify the claim.
$H_o: \mu1=\mu2$
$H_a: \mu1\ne \mu2$ (claim, two tail test)
b. Find the critical value(s).
$\alpha/2=0.01, c=0.98, df=14, |t_c|=2.624, E=2.624\times\sqrt {\frac{3256^2}{15}+\frac{1432^2}{30}}=2310.2$
c. Compute the test value.
$t=\frac{35270-29512-0}{880.4}=6.54$
interval $(35270-29512-2310.2, 35270-29512+2310.2)$ which gives $3447.8\leq \mu1-\mu2\leq 8068.2$
d. Make the decision.
Since $t\gt2.624$, we reject the null hypothesis.
e. Summarize the results.
At α= 0.02 there is a significant difference in teachers’ salaries between the two states.
The 98% confidence interval for the difference of the two means is $3447.8\leq \mu1-\mu2\leq 8068.2$
