2:01A webassign.netn this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in theStudent's t table, use the closest d.s. that is smaller. In some situations, this choice of d.f. may increase the P-value by a smallamount and therefore produce a slightly more "conservative" answer.The western United States has a number of four-lane interstate highways that cut through long tracts of wilderness. To preventcar accidents with wild animals, the highways are bordered on both sides with 12-foot-high woven wire fences. Although thefences prevent accidents, they also disturb the winter migration pattern of many animals. To compensate for this disturbance, thehighways have frequent wilderness underpasses designed for exclusive use by deer, elk, and other animals.In Colorado, there is a large group of deer that spend their summer months in a region on one side of a highway and survive thewinter months in a lower region on the other side. To determine if the highway has disturbed deer migration to the winter feedingarea, the following data were gathered on a random sample of 10 wilderness districts in the winter feeding area. Row B representsthe average January deer count for a 5-year period before the highway was built, and row A represents the average January deercount for a 5-year period after the highway was built. The highway department claims that the January population has notchanged. Test this claim against the claim that the January population has dropped. Use a 5% level of significance. Units used inthe table are hundreds of deer. (Let d-8- A.)1 2 34 s678 9 10B: Before highway 10.1 7.2 12.7 5.6 17.4 9.9 20.5 16.2 18.9 11.6A: After highway 9.1 8.2 10.2 4.1 4.0 7.1 15.2 8.3 12.2 7.3Wilderness District(a) What is the level of significance?State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?O Hoi Ma- 0; H,: 0; two-tailedO Ho: Ma - 0; H,: M> 0; right-tailedO Ho: Hg > 0; H,: M- 0; right-tailedO Ho: Ha- 0; H: Mg < 0; left-tailed(b) What sampling distribution will you use? What assumptions are you making?O The Student's t. We assume that d has an approximately uniform distribution.O The Student's t. We assume that d has an approximately normal distribution.O The standard normal. We assume that d has an approximately uniform distribution.O The standard normal. We assume that d has an approximately normal distribution.What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)O Pvalue > 0.2500.125 < P-value < 0.250O 0.050 < Pvalue <0.125O 0.025 < Pvalue < 0.050O 0.005 < pvalue < 0.025O 0.0005 < P-value < 0.005Sketch the sampling distribution and show the area corresponding to the P-value.A.P-valueP-value-tP-valueP-value-t(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statisticallysignificant at level a?O At the a- 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.O At the a 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.O At the a- 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.O At the a= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.(e) State your conclusion in the context of the application.O Fail to reject the null hypothesis, there is sufficient evidence to claim that the January mean population of deer hasdropped.O Fail to reject the null hypothesis, there is insufficient evidence to claim that the January mean population of deer hasdropped.O Reject the null hypothesis, there is insufficient evidence to claim that the January mean population of deer hasdropped.O Reject the null hypothesis there is sufficient evidence tn claim that the lanuary mean population of deer has dropped.

Name: 2:01A webassign.netn this problem, assume that the distribution of di
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Description: 2:01A webassign.netn this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in theStudent's t table, use the closest d.s. that is smaller. In some situations, this choice of d.f. may

Null Hypothesis: A hypothesis which is tested for plausible rejection is called the Null Hypothesis…

Math

Statistics

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.r. 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. The western United States has a number of four-lane interstate highways that cut through long tracts of wilderness. To prevent car accidents with wild animals, the highways are bordered on both sides with 12-foot-high woven wire fences. Although the fences prevent accidents, they also disturb the winter migration pattern of many animals. To compensate for this disturbance, the highways have frequent wilderness underpasses designed for exclusive use by deer, elk, and other animals. In Colorado, there is a large group of deer that spend their summer months in a region on one side of a highway and survive the winter months in a lower region on the other side. To determine if the highway has disturbed deer migration to the winter feeding area, the following data were gathered on a random sample of 10 wilderness districts in the winter feeding area. Row 8 represents the average January deer count for a 5-year period before the highway was built, and row A represents the average January deer count for a 5-year period after the highway was built. The highway department claims that the January population has not changed. Test this claim against the claim that the January population has dropped. Use a 5% level of significance. Units used in the table are hundreds of deer. (Let d-8- A.) Wilderness District 12 34 5 6 7 D: Before highway 10.1 7.2 12.7 5.6 17.4 9.9 20.5 16.2 18.9 1.6 Ai After highway 9.1 8.2 10.2 4.1 4.0 7.1 15.2 (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Hại M, - 0; H,Mg • 0; two-tailed Hoi Ha- 0, H Hg > 0; right-tailed O Hoi Mg 0; H,M- 0; right-tailed OHgi H- 0; H,: M0; left-tailed (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately uniform distribution. O The Student's t. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the Pvalue. (Round your answer to four decimal places.) Pvalue > 0.250 O 0.125 < Pvalue <0.250 O 0.050 < Pvalue < 0.125 O 0.025 < Pvalue <0.050 O 0.005 < Pvalue < 0.025 O 0.0005 < Pvalue <0.005 Sketch the sampling distribution and show the area corresponding to the P-value. P-value P-value P-value 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? O At the a 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. A O At the a- 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) State your conclusion in the context of the application. O Fail to reject the null hypothesis, there is sufficient evidence to claim that the January mean population of deer has dropped. O Fail to reject the null hypothesis, there is insufficient evidence to claim that the January mean population of deer has dropped. O Reject the null hypothesis, there is insufficient evidence to claim that the January mean population of deer has dropped. O Reject the null hypothesis there issufficient vidence ta daim that the lanuary mean population of deer has dropped.