Anthony Brat is convinced that Seniors really are the most intelligent students on campus. However, nobody will believe him. So he decided to prove this (unquestionable) fact by providing an creative processing test that a psychology professor let him borrow. The test scores from 0 to 80, with 0 being a low score and 80 being a high score. So, Mr. A. Brat went around and administered this test to 8 students from the Freshman, Sophomore, Junior, and Senior classes and got these scores. He received the following scores: Freshman Sophomore Junior Senior 60 60 45 72 63 66 62 59 64 62 67 65 1. What is the null and research hypothesis for this study? 2. What are the degrees of freedom within and the degrees of freedom between? 3. What are the critical values for that statistical test with this data at α = 0.05? α = 0.01?
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.
Anthony Brat is convinced that Seniors really are the most intelligent students on campus. However, nobody will believe him. So he decided to prove this (unquestionable) fact by providing an creative processing test that a psychology professor let him borrow. The test scores from 0 to 80, with 0 being a low score and 80 being a high score. So, Mr. A. Brat went around and administered this test to 8 students from the Freshman, Sophomore, Junior, and Senior classes and got these scores. He received the following scores:
| Freshman | Sophomore | Junior | Senior |
| 60 | 60 | 45 | 72 |
| 63 | 66 | 62 | 59 |
| 64 | 62 | 67 | 65 |
1. What is the null and research hypothesis for this study?
2. What are the degrees of freedom within and the degrees of freedom between?
3. What are the critical values for that statistical test with this data at α = 0.05? α = 0.01?
4. What is your sum of squares within, sum of squares between, and sum of squares total?
5. What is your observed F value?
6. What is your statistical decision?
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