To measure air pollution in a home, let X and Y equal the amount of suspended particulate matter (in μg/m3) measured during a 24-hour period in a home in which there is no smoker and a home in which there is a smoker, respectively. We shall test the null hypothesis H0: σ2X/σ2Y = 1 against the one-sided alternative hypothesis H1: σ2x/σ2Y > 1.
(a) If a random sample of size n = 9 yielded x = 93 and s x = 12.9 while a random sample of size m = 11 yielded y = 132 and sy = 7.1, define a critical region and give your conclusion if α = 0.05.
(b) Now test H0: μX = μY against H1: μX < μY if α = 0.05.