he level of cretaine phosphokinase (CPK) in blood samples measures the amount of muscle damage for athletes. At Jock State University, the level of CPK was determined for each of 25 football players and 15 soccer players before and after practice. The two groups of athletes are trained independently. The data summary is as follows :
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.
he level of cretaine phosphokinase (CPK) in blood samples measures the amount of muscle damage for athletes. At Jock State University, the level of CPK was determined for each of 25 football players and 15 soccer players before and after practice. The two groups of athletes are trained independently. The data summary is as follows :
For football players:
Data for Football players| n=25 | Before Practice | After Practice | Difference (Before-After) |
|---|---|---|---|
| 254.73 | 225.6 | 29.13 | |
| Standard deviation | 115.5 | 132.6 | 21.00 |
For soccer players:
Data for Soccer players| n=15 | Before Practice | After Practice | Difference (Before-After) |
|---|---|---|---|
| Mean | 177.1 | 173.8 | 3.3 |
| Standard deviation | 60.7 | 64.4 | 6.88 |
Assume that all the data above are normal
Test the claim that the mean CPK level has DECREASED for soccer players AFTER exercise (compared to the mean BEFORE exercise), using α=0.10.
AFTER practice, do football players have a DIFFERENT mean CPK values compared to soccer players? Test this claim by performing a hypothesis test, using α=0.10.
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