In: Statistics and Probability
Which z-score formula to use for the question below?
z = x - mean / sd
or z = x - population mean / (sd /sqrt(n))
member_ID | TotalScore |
1 | 26 |
2 | 29 |
3 | 31 |
4 | 23 |
1. Assume sample mean = 7.1 and SD = 3.19, calculate the z-score of each members based on sample mean and SD.
2. Given that population mean = 9.1 and SD = 4.2, calculate the z-score of each members based on the population mean and SD.
If we are to determine how far each score is from its mean (sample / population), we need to go for Z score for individual observations 'x'; the formula is given by,
......................(for sample mean and sample SD)
......................(for population mean and population SD)
Here, we have to find the Z scores for these individual values:
1. For
Member 1:
Member 2:
Member 3:
Member 4:
2. For
Member 1:
Member 2:
Member 3:
Member 4:
However, if we are to determine how far a sample mean score is from its population mean, then Score changes to means score () and since the standard error of mean is SD / , SD changes to SE ().The Z score would then be defined as:
Suppose, we were to determine the Z score of the sample mean, where, (say), then,