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.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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.)
| A | B | Difference= A-B |
| 132 | 127 | 5 |
| 109 | 118 | -9 |
| 126 | 139 | -13 |
| 124 | 102 | 22 |
| 102 | 103 | -1 |
| 96 | 107 | -11 |
| 100 | 109 | -9 |
| 131 | 117 | 14 |
| 97 | 105 | -8 |
| 120 | 110 | 10 |
| 115 | 109 | 6 |
| 98 | 105 | -7 |
| 111 | 109 | 2 |
| 93 | 104 | -11 |
| 97 | 102 | -5 |
| 111 | 100 | 11 |
| 110 | 106 | 4 |
| 92 | 103 | -11 |
| 85 | 98 | -13 |
| 109 | 102 | 7 |
| 123 | 100 | 23 |
| 115 | 95 | 20 |
| 107 | 93 | 14 |
| 96 | 98 | -2 |
| 108 | 93 | 15 |
| 104 | 90 | 14 |
| 128 | 108 | 20 |
| 121 | 102 | 19 |
| 85 | 96 | -11 |
| 91 | 92 | -1 |
| 115 | 108 | 7 |
| 114 | 117 | -3 |
| 86 | 109 | -23 |
| 115 | 107 | 8 |
| 90 | 100 | -10 |
| 113 | 95 | 18 |
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