# Chapter 9 - Testing the Difference Between Two Means, Two Proportions, and Two Variances - Review Exercises - Section 9-2 - Page 541: 5

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 $3447.8\leq \mu1-\mu2\leq 8068.2$

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