The following data show the rankings of 11 states based on expenditure per student (ranked 1 highest to 11 lowest) and student-teacher ratio (ranked 1 lowest to 11 highest). State Expenditure per Student Student-Teacher Ratio Arizona 9 10 Colorado 5 8 Florida 4 6 Idaho 2 11 Iowa 6 4 Louisiana 11 3 Massachusetts 1 1 Nebraska 7 2
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.
| State | Expenditure per Student |
Student-Teacher Ratio |
|---|---|---|
| Arizona | 9 | 10 |
| Colorado | 5 | 8 |
| Florida | 4 | 6 |
| Idaho | 2 | 11 |
| Iowa | 6 | 4 |
| Louisiana | 11 | 3 |
| Massachusetts | 1 | 1 |
| Nebraska | 7 | 2 |
| North Dakota | 8 | 7 |
| South Dakota | 10 | 5 |
| Washington | 3 | 9 |
Ha: ρs < 0H0: ρs ≠ 0
Ha: ρs = 0 H0: ρs = 0
Ha: ρs ≠ 0H0: ρs ≤ 0
Ha: ρs > 0H0: ρs > 0
Ha: ρs = 0
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