Based on information from The Denver Post, a random sample of n₁ = 12 winter days in Denver gave a sample mean pollution index of x̅₁ = 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 x̅₂ = 36. Previous studies show that σ₂ = 15. Assume the pollution index is normally distributed in both Englewood and Denver. 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.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding z or t value as appropriate.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signi­ficant at level a?

(e) Interpret your conclusion in the context of the application.

For degrees of freedom d.f. not in the Student’s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and therefore produce a slightly more “conservative” answer.

Answers may vary due to rounding.