A new drug’s effectiveness in lowering blood pressure is to be tested against a placebo. The random variable denotes the amount that the new drug lowers blood pressure and the random variable denotes the amount that the placebo lowers blood pressure. and are a normal random variables with unknown means and and variances 2 and 2 , respectively. A random sample of 10 people is given the new drug, let 1, 2, ... , 10 denote the amount each of their blood pressure was lowered by, and a random sample of 15 people is given the placebo, let 1, 2, ... , 15 denote the amount each of their blood pressure was lowered by.
The observed values of the sample gives = 35, = 25, 2 = 50, and 2 = 55. At an = .1 level, is the variance 2 different than 2 ?