Use the three-read strategy to understand the following exercise from a statistics textbook, and then proceed to complete the exercise. A popular urban legend is that more babies than usual are born during certain phases of the lunar cycle, especially near the full moon. Suppose that a certain paper classified births according to the lunar cycle. Data for a sample of randomly selected births, consistent with summary quantities in the paper, are given in the accompanying table. Lunar Phase Number of Days Number of Births New Moon 24 7,670 Waxing Crescent 152 48,442 First Quarter 24 7,589 Waxing Gibbous 149 47,814 Full Moon 24 7,711 Waning Gibbous 150 47,595
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.
| Lunar Phase | Number of Days |
Number of Births |
|---|---|---|
| New Moon | 24 | 7,670 |
| Waxing Crescent | 152 | 48,442 |
| First Quarter | 24 | 7,589 |
| Waxing Gibbous | 149 | 47,814 |
| Full Moon | 24 | 7,711 |
| Waning Gibbous | 150 | 47,595 |
| Last Quarter | 24 | 7,733 |
| Waning Crescent | 152 | 48,240 |
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