In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of...

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In this problem, assume that the distribution of differences is approximately normal. 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 by a small amount and therefore produce a slightly more "conservative" answer. In the following data pairs, A represents birth rate and B represents death rate per 1,000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information. A: 12.6 13.4 12.8 12.1 11.4 11.1 14.2 15.1 B: 9.5 14.3 10.7 14.2 13.2 12.9 10.9 10.0 A: 12.5 12.3 13.1 15.8 10.3 12.7 11.1 15.7 B: 14.1 13.6 9.1 10.2 17.9 11.8 7.0 9.2 Do the data indicate a difference (either way) between population average birth rate and death rate in this region? Use a = 0.01. (Let d = A - B.) (a) What is the level of significance? 0.01 State the null and alternate hypotheses (in per 1,000 resident population). (Enter != for as needed.) Ho H: Will you use a left-tailed, right-tailed, or two-tailed test? 00 two-tailed left-tailed right-tailed (b) What sampling distribution will you use? What assumptions are you making? We'll use the standard normal. We assume that d has an approximately normal distribution. We'll use the Student's t. We assume that d has an approximately uniform distribution. We'll use the Student's t. We assume that d has an approximately normal distribution. We'll use the standard normal. We assume that d has an approximately uniform distribution. (b) What sampling distribution will you use? What assumptions are you making? 000 We'll use the standard normal. We assume that d has an approximately normal distribution. We'll use the Student's t. We assume that d has an approximately uniform distribution. We'll use the Student's t. We assume that d has an approximately normal distribution. We'll use the standard normal. We assume that d has an approximately uniform distribution. What is the t value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value <0.010 Sketch the sampling distribution and show the area corresponding to the P-value. 0-4 -4 A -2 0 2 -2 2 70-4 -2 0 2 -2 0 2 i (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? 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. 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 reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence to claim that the average birth and death rates are different in this region. Reject the null hypothesis, there is insufficient evidence to claim that the average birth and death rates are different in this region. Fail to reject the null hypothesis, there is sufficient evidence to claim that the average birth and death rates are different in this region. Fail to reject the null hypothesis, there is insufficient evidence to claim that the average birth and death rates are different in this region. In this problem, assume that the distribution of differences is approximately normal. 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 by a small amount and therefore produce a slightly more "conservative" answer. In the following data pairs, A represents birth rate and B represents death rate per 1,000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information. A: 12.6 13.4 12.8 12.1 11.4 11.1 14.2 15.1 B: 9.5 14.3 10.7 14.2 13.2 12.9 10.9 10.0 A: 12.5 12.3 13.1 15.8 10.3 12.7 11.1 15.7 B: 14.1 13.6 9.1 10.2 17.9 11.8 7.0 9.2 Do the data indicate a difference (either way) between population average birth rate and death rate in this region? Use a = 0.01. (Let d = A - B.) (a) What is the level of significance? 0.01 State the null and alternate hypotheses (in per 1,000 resident population). (Enter != for as needed.) Ho H: Will you use a left-tailed, right-tailed, or two-tailed test? 00 two-tailed left-tailed right-tailed (b) What sampling distribution will you use? What assumptions are you making? We'll use the standard normal. We assume that d has an approximately normal distribution. We'll use the Student's t. We assume that d has an approximately uniform distribution. We'll use the Student's t. We assume that d has an approximately normal distribution. We'll use the standard normal. We assume that d has an approximately uniform distribution. (b) What sampling distribution will you use? What assumptions are you making? 000 We'll use the standard normal. We assume that d has an approximately normal distribution. We'll use the Student's t. We assume that d has an approximately uniform distribution. We'll use the Student's t. We assume that d has an approximately normal distribution. We'll use the standard normal. We assume that d has an approximately uniform distribution. What is the t value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value <0.010 Sketch the sampling distribution and show the area corresponding to the P-value. 0-4 -4 A -2 0 2 -2 2 70-4 -2 0 2 -2 0 2 i (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? 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. 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 reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence to claim that the average birth and death rates are different in this region. Reject the null hypothesis, there is insufficient evidence to claim that the average birth and death rates are different in this region. Fail to reject the null hypothesis, there is sufficient evidence to claim that the average birth and death rates are different in this region. Fail to reject the null hypothesis, there is insufficient evidence to claim that the average birth and death rates are different in this region.