Let X and Y equal the number of milligrams of tar in filtered and nonfiltered
Chapter 8, Problem 8.2-7(choose chapter or problem)
Let X and Y equal the number of milligrams of tar in filtered and nonfiltered cigarettes, respectively. Assume that the distributions of X and Y are N(X , 2 X ) and N(Y , 2 Y ), respectively. We shall test the null hypothesis H0: X Y = 0 against the alternative hypothesis H1: X Y < 0, using random samples of sizes n = 9 and m = 11 observations of X and Y, respectively. (a) Define the test statistic and a critical region that has an = 0.01 significance level. Sketch a figure illustrating this critical region. (b) Given n = 9 observations of X, namely, 0.9 1.1 0.1 0.7 0.4 0.9 0.8 1.0 0.4 and m = 11 observations of Y, namely, 1.5 0.9 1.6 0.5 1.4 1.9 1.0 1.2 1.3 1.6 2.1 calculate the value of the test statistic and state your conclusion clearly. Locate the value of the test statistic on your figure.
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