Among the data collected for the World Health Organization air quality monitoring project is a measure of suspended particles in g/m3 . Let X and Y denote the concentration of suspended particles in the city center (commercial district), for Melbourne and Houston, respectively. Using 13 observations of X (Melbourne) and 16 observations of Y (Houston), we would like to conduct the following test at 0.05 level: H0 : X = Y , H1 : X < Y .

1.Given the following summary statistics: x = 72.9 Sx = 25.6, y = 81.7, Sy = 28.3, conduct the test of hypothesis. Report the decision rule and the P-value to make a conclusion and interpret your results in the context of the problem.

2.Find a 95% CI for Y X. Explain if and how your result confirms the conclusion for the test of part (a).

3.Conduct a test to determine if the assumption of equal variances (versus a two sided alternative) considered in part (a) is valid. State the null and alternative hypotheses. Discuss the implications of your findings regarding the conclusions of the previous parts.

4.Confirm the result of part (c) using a 95% confidence interval.