Among the data collected for the World Health Organization air quality monitoring project is a measure of suspended particles, in μg/m3. Let X and Y equal the concentration of suspended particles in μg/m3 in the city centers (commercial districts), of Melbourne and Houston, respectively. Using n = 13 observations of X and m = 16 observations of Y, we shall test H0: μX = μY against H1: μX < μY.
(a) Define the test statistic and critical region, assuming that the variances are equal. Let α = 0.05.
(b) If = 72.9, sx = 25.6, = 81.7, and sy = 28.3, calculate the value of the test statistic and state your conclusion.
(c) Give bounds for the p-value of this test.