Do the data indicate that the U.S. population mean cost of living index for utilities is less than that for transportation in these areas? Use ? = 0.05. (Let d = A − B.) (a) What is the level of significance? What is the value of the sample test statistic?
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 utilities and B represents the cost of living index for transportation. The data are paired by metropolitan areas in the United States. A random sample of 46 metropolitan areas gave the following information.
| A: | 91 | 84 | 83 | 107 | 81 | 100 | 91 | 126 | 106 |
| B: | 101 | 93 | 105 | 105 | 108 | 110 | 94 | 113 | 112 |
| A: | 118 | 133 | 104 | 84 | 80 | 77 | 90 | 92 | 90 |
| B: | 106 | 95 | 110 | 112 | 105 | 93 | 119 | 99 | 109 |
| A: | 106 | 95 | 110 | 112 | 105 | 93 | 119 | 99 | 109 |
| B: | 96 | 109 | 103 | 107 | 103 | 102 | 101 | 86 | 94 |
| A: | 109 | 113 | 90 | 121 | 120 | 85 | 91 | 91 | 97 |
| B: | 88 | 100 | 104 | 119 | 116 | 104 | 121 | 108 | 86 |
| A: | 95 | 115 | 99 | 86 | 88 | 106 | 80 | 108 | 90 | 87 |
| B: | 100 | 83 | 88 | 103 | 94 | 125 | 115 | 100 | 96 | 127 |
Do the data indicate that the U.S. population mean cost of living index for utilities is less than that for transportation in these areas? Use ? = 0.05. (Let d = A − B.)
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