A random sample ofn₁=18winter days in Denver gave a sample mean pollution indexx₁=43. Previous studies show that₁=11. For Englewood (a suburb of Denver), a random sample ofn₂=14winter days gave a sample mean pollution index ofx₂=52. Previous studies show that₂=12. 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.

H₀:₁<₂;H₁:₁=₂

H₀:₁=₂;H₁:₁>₂

H₀:₁=₂;H₁:₁₂

H₀:₁=₂;H₁:₁<₂

(b) What sampling distribution will you use? What assumptions are you making?

The Student'st. We assume that both population distributions are approximately normal with known standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to two decimal places.)

(c) Find (or estimate) theP-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to theP-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?

At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

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

Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Reject the null hypothesis, there is insufficient evidence that there is a