Null Hypothesis:
\(\displaystyle{H}_{{0}}:\) There is no sufficient evidence that the state A residents vary more than amounts from state B residents.
Alternative Hypothesis:
\(\displaystyle{H}_{{0}}:\) There is a sufficient evidence that the state A residents vary more than amounts from state B residents.
Test statistic:
Excel Procedure:
Enter the data for ‘State A’ and ‘State B’ in Excel sheet>Data>Data Analysis>F test two-samples for variances’ and click on ‘OK’>Select the column of ‘State A’ under ‘Variable 1 Range’>Select the column of ‘State B’ under ‘Variable 2 Range’>Click on ‘OK’.
Exel Output:
\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{F}-{t}{e}{s}{t}\ {t}{w}{o}-{S}{a}\mp\le\ {f}{\quad\text{or}\quad}\ {V}{a}{r}{i}{a}{n}{c}{e}{s}\backslash{h}{l}\in{e}\backslash&{S}{t}{a}{t}{e}{A}&{S}{t}{a}{t}{e}{B}\backslash{h}{l}\in{e}{M}{e}{a}{n}&{147.5833333}&{136.75}\backslash{V}{a}{r}{i}{a}{n}{c}{e}&{116.6287879}&{26.38636364}\backslash{O}{b}{s}{e}{r}{v}{a}{t}{i}{o}{n}{s}&{12}&{12}\backslash{d}{f}&{11}&{11}\backslash{F}&{4.420040195}&\backslash{p}{\left({F}\Leftarrow{f}\right)}{o}\ne-{t}{a}{i}{l}&{0.010391966}&\backslash{F}{C}{r}{i}{t}{i}{c}{a}{l}{o}\ne-{t}{a}{i}{l}&{2.81793047}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
From the output, F = 4,42
P value = 0.10
Decision Rule:
If P-value \(\displaystyle\leq\alpha\), then reject the null hypothesis.
Conclusion:
Let consider the level of significance is \(\displaystyle\alpha={0.05}\)
Here, the p-value is less than the level of significance.
From the rejection rule, reject the null hypothesis.
Conclusion: There is a sufficient evidence that the state A residents vary more than amounts from state B residents.