Do short problems 17In this problem, assume that the distribution of differences is approximately normal. Note: For degrees offreedom d.f. not in the Student's ttable, use the closest d.f. that is smaller. In some situations, this choiceof d. f. may increase the P-value by a small amount and therefore produce a slightly more "conservative"answer.Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak windgusts (in miles per hour) for January and April are recorded below.Wilderness District23451341316478JanuaryApril111108 8861USE SALT113195Does this information indicate that the peak wind gusts are higher in January than in April? Use a =0.01. Solve the problem using the critical region method of testing. (Let d= January - April. Round youranswers to three decimal places.)test statistic =critical value=Interpret your conclusion in the context of the application.Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher inJanuary. Fail to reject the null hypothesis, there is insufficient evidence to claim average peak windgusts are higher in January. Reject the null hypothesis, there is insufficient evidence to claimaverage peak wind gusts are higher in January. Fail to reject the null hypothesis, there is sufficientevidence to claim average peak wind gusts are higher in January.Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?We reject the null hypothesis using the P-value method, but fail to reject using the critical region method.We reject the null hypothesis using the critical region method, but fail to reject using the P-valuemethod. The conclusions obtained by using both methods are the same. 4A random sample of m= 10 regions in New England gave the following violent crime rates (per millionpopulation).X₁: New England Crime Rate3.3 3.9 4.2 4.1 3.3 4.11.8 4.8 2.9 3.1Another random sample of m2 = 12 regions in the Rocky Mountain states gave the following violent crimerates (per million population).X2: Rocky Mountain Crime Rate3.5 4.1 4.7 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8USE SALTAssume that the crime rate distribution is approximately normal in both regions. Do the data indicate thatthe violent crime rate in the Rocky Mountain region is higher than in New England? Use x = 0.01. Solvethe problem using both the traditional method and the P-value method. (Test the difference μ 1-μ2.Round the test statistic and critical value to three decimal places.)test statisticcritical valueFind (or estimate) the P-value.P-value > 0.250 0.125 < P-value < 0.2500.005 < P-value < 0.025 P-value < 0.0050.050 P-value < 0.125 0.025 < P-value < 0.050ConclusionFail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountainregion is higher than in New England. Reject the null hypothesis, there is sufficient evidence thatviolent crime in the Rocky Mountain region is higher than in New England. Fail to reject the nullhypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than inNew England. Reject the null hypothesis, there is insufficient evidence that violent crime in the RockyMountain region is higher than in New England.Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?The conclusions obtained by using both methods are the same. We reject the null hypothesis usingthe traditional method, but fail to reject using the P-value method. These two methods differ slightly.We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.

Widerness District January April 1 131 95 2 134 111 3 131 108 4 64 88 5 78 61 We…

17 In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's ttable, 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. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Wilderness District 3 131 January April 108 USE SALT 1 31 131 95 2 134 111 4 5 64 78 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use x = 0.01. Solve the problem using the critical region method of testing. (Let d= January - April. Round your answers to three decimal places.) test statistic critical value= Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? We reject the null hypothesis using the P-value method, but fail to reject using the critical region method. We reject the null hypothesis using the critical region method, but fail to reject using the P-value

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P