Random samples of LaTeX: n_1=15n1=15 and LaTeX: n_2= 10n2=10 were selected from populations 1 and 2, respectively. The corresponding sample standard deviations were LaTeX: s_1= 5.3s1=5.3 and LaTeX: s_2= 8.8s2=8.8.
a) Do the data provide sufficient evidence (LaTeX: alpha=0.05α=0.05) to indicate a difference in LaTeX: sigma_1σ1 and LaTeX: sigma_2σ2? Use rejection region approach.
b) Place a 95% confidence interval on the ratio of the variances LaTeX: sigma^{2}_{1}/sigma^{2}_{2}σ21/σ22.
c) What assumptions have you made concerning the data and populations when making your calculations in parts (a) and (b)?