A random sample of n = 19. For Englewood (a suburb of Denver), a random sample of n = 12 = 10 winter days in Denver gave a sample mean pollution index x = 43. Previous studies show that = 11. Assume the pollution index is normally distributed in both Englewood and Denver. winter days gave a sample mean pollution index of x2 = 33. Previous studies show that 2 (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. (i) What is the level of significance? State the null and alternate hypotheses. (Enter != for as needed.) Ho H: (ii) What sampling distribution will you use? What assumptions are you making? It follows the standard normal sampling distribution. We assume that both population distributions are approximately normal with unknown standard deviations. It follows the Student's t sampling distribution. We assume that both population distributions are approximately normal with unknown standard deviations. It follows the Student's t sampling distribution. We assume that both population distributions are approximately normal with known standard deviations. It follows the standard normal sampling distribution. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? Compute the corresponding z or t-value as appropriate. (Test the difference - 2. Round your answer to two decimal places.) (iii) Find (or estimate) the P-value. (Round your answer to four decimal places.) (iii) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 (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? At the = = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. 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 difference in mean pollution index for Englewood and Denver. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (b) Find a 99% confidence interval for - 2. (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your answers to two decimal places.) Explain the meaning of the confidence interval in the context of the problem. O Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver. Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver. Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver. Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.