A Coach found the correlation between physical fitness and athletic ability to be r=.65. the mean and standard deviation of the physical fitness test was 330, 50. the mean and standard deviation of the athletic ability test was 9, 2. If you have a physical fitness score of 350, what will be the athletic ability score?
To find the athletic ability score corresponding to a physical fitness score of 350, you need to use the correlation coefficient and the mean and standard deviation of both variables. Here's how to do it:
Step 1: Write down the given information:
- Correlation coefficient (r) between physical fitness and athletic ability: r = 0.65
- Mean of the physical fitness test: mean_physical_fitness = 330
- Standard deviation of the physical fitness test: sd_physical_fitness = 50
- Mean of the athletic ability test: mean_athletic_ability = 9
- Standard deviation of the athletic ability test: sd_athletic_ability = 2
Step 2: Standardize the physical fitness score:
The first step is to standardize the physical fitness score of 350 using the given mean and standard deviation:
z_score = (x - mean_physical_fitness) / sd_physical_fitness
z_score = (350 - 330) / 50
z_score = 20 / 50
z_score = 0.4
Step 3: Use the correlation coefficient to find the standardized athletic ability score:
The correlation coefficient relates the standardized scores of the two variables. Since we have the z-score of physical fitness (0.4), we can use it to find the corresponding z-score for athletic ability.
r = correlation coefficient
z_athletic_ability = r * z_physical_fitness
z_athletic_ability = 0.65 * 0.4
z_athletic_ability = 0.26
Step 4: Convert the standardized athletic ability score back to the original scale:
To get the original athletic ability score, we need to convert the standardized score (z_athletic_ability) back to the original scale using the mean and standard deviation of the athletic ability test.
athletic_ability = (z_athletic_ability * sd_athletic_ability) + mean_athletic_ability
athletic_ability = (0.26 * 2) + 9
athletic_ability = 0.52 + 9
athletic_ability = 9.52
Therefore, if you have a physical fitness score of 350, the corresponding athletic ability score would be approximately 9.52.