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 the cost of living index for housing and B represents the cost of living index for groceries. The data are paired by metropolitan areas in the United States. A random sample of 36 metropolitan areas gave the following information. A: 132 109 126 124 102 96 100 131 97 B: 127 118 139 102 103 107 109 117 105 A: 120 115  98 111  93  97 111 110  92 B: 110 109 105 109 104 102 100 106 103 A:   85 109 123 115 107   96 108 104 128 B:   98 102 100   95   93   98   93   90 108 A: 121   85   91 115 114   86 115   90 113 B: 102   96   92 108 117 109 107 100   95     What is the value of the sample test statistic? (Round your answer to three decimal places.)

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 1 2 3 4 January April 130 127 122 64 78 105 97 108 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 Reject the null hypothesis, there is insufficient evidence to claim average peak…

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.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. Weather Station 1 2 3 4 5 January 137 124 128 64 78 April 104 115 102 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. (Let d = January − April.) (a) What is the level of significance? What is the value of the sample test statistic?

Here is a data set summarized as a stem-and-leaf plot: Stem Leaf 6 1 2 2 3 4 9 7 2 2 2 2 4 9 9 8 4 7 9 5 6 9 Key: 4|5 = 45 How many data values are in this data set? What is the minimum value in the last class? How many of the original values are greater than or equal to 80? What percent of values are greater than or equal to 80? Answer with a percentage rounded to the nearest whole number.