Scenario: Suppose you have a sample of 65 juveniles arrested by the local police department over the past six months. You have a distribution of scores that represent the number of prior offenses committed by this sample. The metric of measurement is number of arrests.
- What is the level of measurement?
Mean and standard deviation: For this sample, the mean number of prior arrests is 4.8 and the standard deviation is 3.25. For an analysis, a z-score would be calculated for each raw score.
- What is the z-score for a raw score of 3?
- What is the z-score for a raw score of 6?
- Explain the sign and magnitude for the z-score for your raw score of 3.
- Explain the sign and magnitude for the z-score for your raw score of 6.
Probability: Using the z-table (accessed at http://www.z-table.com):
- Find the area (probability) for the z-score for your raw score of 3.
- Find the area (probability) for the z-score for your raw score of 6.
- What are the conclusions you can draw for the probability associated with your raw score of 3?
- What are the conclusions you can draw for the probability associated with your raw score of 6?
- How would you use this information in making a decision to reject a null hypothesis?
- Could you use a t-test for this sample size/example? Why or why not?
Sample Solution