Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. Predictor Coef SE Coef T P Constant -0.182 2.429 -0.09 0.929 Diameter 0.7824 0.1281 5.33 0.003 S = 3.92430 R-Sq = 71.4%
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.
Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data.
| Predictor | Coef | SE Coef | T | P |
| Constant | -0.182 | 2.429 | -0.09 | 0.929 |
| Diameter | 0.7824 | 0.1281 | 5.33 | 0.003 |
| S = 3.92430 | R-Sq = 71.4% |
(b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is Se/√Σx2 – (1/n)(Σx)2. From the Minitab display, what is the value of the standard error for the slope b?
(c) The formula for the margin of error E for a c% confidence interval for the slope β can be written as E = tc(SE Coef). The Minitab display is based on n = 12 data pairs. Find the critical value tc for a 90% confidence interval in the relevant table. Then find a 90% confidence interval for the population slope β. (Use 3 decimal places.)
| tc | |
| lower limit | |
| upper limit |
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