When an entire population or sample's raw scores are transformed into \( Z \) scores the mean of the \( Z \) scores will be zero.

Yes, that is correct! When you transform a set of raw scores into \( Z \) scores, the mean of the \( Z \) scores will always be zero. This is because the \( Z \) score is calculated using the formula: \[ Z = \frac{(X - \mu)}{\sigma} \] where \( X \) is a raw score, \( \mu \) is the mean of the raw scores, and \( \sigma \) is the standard deviation of the raw scores. When you calculate the \( Z \) scores for all the raw scores in a population or sample, the transformation effectively centers the data around the mean. Since the \( Z \) scores represent how many standard deviations a raw score is from the mean, the positive and negative \( Z \) scores will balance out, resulting in a mean of zero for the \( Z \) scores. In summary, transforming raw scores to \( Z \) scores standardizes the data, and the mean of the resulting \( Z \) scores will always be zero.