Question

A toacher's union would like to soe if there is a difference in the variability of the salaries eamed 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 complete parts a and b. given below to County 1 County 2 $4,000 $2,700 Sample standard deviation Sample size 30 30 Uoing 0.10,Gotermine it hero is a diference n the variablily of the salaries in the lwo counties dentify the null and alternative hypotheses. a, Using ?-0.10, determine if there is a difference in the Calculate the appropriate test statistic. The test statistic is (Round to two decimal places as needed.) Determine the appropriate critical valuels) The critical value(o) is(are) (Round to three decimal places as neded Use a comma to separate answers as needed.) ?1 the null hypothesis. There is evidence that the population variance for County 1 is V the population variance for County2 b. Use technology to find the p-value and interpret the result The p-value is Round to three decimal places as needed.) Enter your answer in each of the answer boxes.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: ?₁² = ?₂²

Alternative hypothesis H_A: ?₁² $\neq$ ?₂²

Formulate an analysis plan. For this analysis, the significance level is 0.10.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (F).

DF₁ = n₁ - 1 = 30 -1

D.F₁ = 29

DF₂ = n₂ - 1 = 30 -1

D.F₂ = 29

Test statistics:-

$F = \frac{s_{1}^{2}}{s_{2}^{2}}$

F = 2.195

F_critical = 1.62

Since the first sample had thelarger standard deviation, this is a right-tailed test.

p value for the F distribution = 0.019

Interpret results. Since the P-value (0.019) is less than the significance level (0.10), we have to reject the null hypothesis.