Based on information from the Rocky Mountain News, a random sample of n1 = 12 winter days in Denver gave a sample mean pollution index of 1 = 43. Previous studies show that σ1 = 21. For Englewood (a suburb of Denver), a random sample of n2 = 14 winter days gave a sample mean pollution index of 2 = 36. Previous studies show that σ2 = 15. Assume the pollution index is normally distributed in both Englewood and Denver.
(a) Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance.
(b) Find a 99% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.
Please provide the following information for problem part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) – (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(v) Interpret your conclusion in the context of the application.