A researcher was interested in estimating the relationship between SAT scores and first year GPA. He looked at the data from a university which requires minimum SAT scores of 600 to enter the university (Note. The possible SAT score is between 200-800). The data from this experiment are presented below. Student ID SAT(X) GPA (Y) 1 680 2.4 2 745 2.1 3 670 2.2 4 720 2.5 5 653 2.0 6 710 1.8 7 675 1.8 8 634 2.3 9 690 2.4 10 711 2.3 Mean 688.8 2.18 Variance 1109 0.06 = (X −X)(Y−Y) 3.15 Compute the Pearson correlation (r) and interpret the coefficient in terms of the direction (positive or negative) and strength of the relationship (weak, moderate, or strong)
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.
A researcher was interested in estimating the relationship between SAT scores and first year GPA. He looked at the data from a university which requires minimum SAT scores of 600 to enter the university (Note. The possible SAT score is between 200-800). The data from this experiment are presented below.
|
Student ID |
SAT(X) |
GPA (Y) |
|
1 |
680 |
2.4 |
|
2 |
745 |
2.1 |
|
3 |
670 |
2.2 |
|
4 |
720 |
2.5 |
|
5 |
653 |
2.0 |
|
6 |
710 |
1.8 |
|
7 |
675 |
1.8 |
|
8 |
634 |
2.3 |
|
9 |
690 |
2.4 |
|
10 |
711 |
2.3 |
|
Mean |
688.8 |
2.18 |
|
Variance |
1109 |
0.06 |
=
(X −X)(Y−Y)
3.15
- Compute the Pearson
correlation (r) and interpret the coefficient in terms of the direction (positive or negative) and strength of the relationship (weak, moderate, or strong)
- Many previous studies have found that there is a strong positive relationship between SAT score and the first year GPA. Is your conclusion from question (a) consistent with the previous studies? If not, explain what factor(s) might cause the correlation in this sample to be small.
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