1.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.

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.

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. 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 4 5 January 123 132 125 64 78 April 95 110 108 88 61 Does 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 your answers to three decimal places.) test statistic = critical value = Interpret your conclusion in the context of the application. O Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. O Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. O Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. O Fail to reject the null hypothesis, there is insufficient 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? O We reject the null hypothesis using the critical region method, but fail to reject using the P-value method. The conclusions obtained by using both methods are the same. O We reject the null hypothesis using the P-value method, but fail to reject using the critical region method.A random sample of n, = 16 communities in western Kansas gave the following information for people under 25 years of age. x1: Rate of hay fever per 1000 population for people under 25 96 92 119 127 93 123 112 93 125 95 125 117 97 122 127 8 A random sample of n, = 14 regions in western Kansas gave the following information for people over 50 years old. x7: Rate of hay fever per 1000 population for people over 50 94 109 99 96 110 88 110 79 115 100 89 114 85 96 USE SALT i) Use a calculator to calculate x1, S1, x2, and $2. (Round your answers to four decimal places.) X 7 (ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use a = 0.05. a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 = H2; H1: H1 = H2 O Ho: H1 > #2i H1: M1 = Hz O Ho: H1 = H2; H1: M1 > Hz O Ho: M1 = H2i H1: H1 * Hz (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal. 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. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Test the difference #1 - #2. Round your answer to three decimal places.)(c) Find (or estimate) the P-value. O P-value > 0.250 O 0.125 0; H1: My = 0; right- tailed O Ho: My = 0; H1: My # 0; two-tailed O Ho: My = 0; H1: My > 0; right-tailed (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that d has an approximately uniform distribution. The standard normal. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately normal distribution. O The Student's t. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. O P-value > 0.250 O 0.125 0; H1: Mg = 0; right-tailed O Ho: My = 0; H1: My 0; right-tailed O Ho: Hd = 0; H1: Mg * 0; two-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 normal distribution. O The standard normal. We assume that d has an approximately normal distribution. O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. O P-value > 0.250 O 0.125 0; right- tailed O Ho: Hd = 0; H1: My 0; H1: Ud = 0; right-tailed O Ho: My = 0; H1: Mg # 0; two-tailed (b) What sampling distribution will you use? What assumptions are you making? 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. 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. What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Find (or estimate) the P-value. O P-value > 0.250 O 0.125 H2 (c) Compute X 1 - X2. * 1 - * 2 = Compute the corresponding sample distribution value. (Test the difference #1 - #2. Round your answer to three decimal places.) (d) Estimate the P-value of the sample test statistic. O P-value > 0.500 O 0.250