Given: \(S1= 5.67\)

\(S2 = 3.18\)

\(n1 =n2 =10\)

\(\alpha=0.05\)

Claim: Different

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis and the alternative hypothesis state the opposite of exch other. The null hypothesis needs to contain an equality.

\(H0: \sigma(\frac{2}{1}) = \sigma(\frac{2}{2})\)

\(Ha: \sigma(\frac{2}{1}) \neq \sigma(\frac{2}{2})\)

Compute the value of the test statistic: \(F=\frac{S\frac{2}{1}}{S\frac{2}{2}}=\frac{5.67^2}{3.18^2}\sim3.1792\)

The critical value is given in the F-distribution table in the appendix in the row with \(dfd = n2 -1 = 10-1=9\) and in the column with \(dfn = n1 -1 =10-1=9\):

\(f0.025.9.9 = 0.248\)

\(f0.0975.9.9 = 4.03\)

The rejection region contains all values smaller than 0.248 and all values larger than 4.03.

If the value of the test statistic is in the rejection region, then reject the null hypothesis: \(0.248 < 3.1792 < 4.03 \Rightarrow\) Fail to reject H0

There is not sufficient evidence to support the claim that the variances are significantly different