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 birth rate and B represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information.
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 birth rate and B represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information.
| A: | 12.5 | 13.2 | 12.6 | 12.1 | 11.4 | 11.1 | 14.2 | 15.1 |
| B: | 9.6 | 14.3 | 10.7 | 14.2 | 13.2 | 12.9 | 10.9 | 10.0 |
| A: | 12.5 | 12.3 | 13.1 | 15.8 | 10.3 | 12.7 | 11.1 | 15.7 |
| B: | 14.1 | 13.6 | 9.1 | 10.2 | 17.9 | 11.8 | 7.0 | 9.2 |
Do the data indicate a difference (either way) between population average birth rate and death rate in this region? Use ? = 0.01. (Let d = A − B.)
What is the value of the sample test statistic? (Round your answer to three decimal places.)
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