Question

A teacher's union would like to see if there is a difference in the variability of the salaries earned by high school teachers in one county as compared to another. A random sample of teacher salaries from each county was selected, and the standard deviation of each sample was calculated. Use the information given below to complete parts a and b. County 1 County 2 Sample standard deviation $3,600 $2,500 Sample size 25 25 a. Using a =0.10, determine if there is a difference in the variability of the salaries in the two counties. Identify the null and alternative hypotheses. Hoio H₂:0 oz lo Calculate the appropriate test statistic. The test statistic is (Round to two decimal places as needed.) Determine the appropriate critical value(s). The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.) the null hypothesis. There is evidence that the population variance for County 1 is the population variance for County 2.

Answer 1

We have

s1=$3600 , n1=25

s2$2500,. n2=25

a)

Alpha=0.10

Setting up hypothesis:

Ho:sigma1²= sigma2²

H1: sigma1²≠sigma2²

##)Calculate the test statistic:

Test statistic (f)= s1²/s2²=3600²/2500²=2.0776≈2.08

#critical value

Df1= 24,. Df2 = 24

Thus Critical value are =(0.504,1.984)

##)since the test is greater than criticalvalue values.

Reject the null hypothesis,there is sufficient evidence to conclude that the population variance of country 1 is different from the population variance for country 2

b)

The p value is =0.0395≈0.039

The p value is less than 0.10, we Reject the null hypothesis.

Ans→the p value is less than 0.10, Reject the null hypothesis, there is sufficient evidence to conclude that the population variance for country 1 is different from country 2.

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