Textbook Problem

Please provide the following information for Problems 11-22. part (a):

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

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

(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 a?

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

Note: 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.

Environment: Pollution Index Based on information from the Denver Post, a random sample of $n_1=12$ winter days in Denver gave a sample mean pollution index of ${\bar{x}}_1=43$. Previous studies show that ${\sigma }_1=21$. For Englewood (a suburb of Denver), a random sample of $n_2=14$ winter days gave a sample mean pollution index of ${\bar{x}}_2=36$. Previous studies show that ${\sigma }_2=21$. 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 ${\mu }_1-{\mu }_2$. Explain the meaning of the confidence interval in the context of the problem.