## Question 464:

1

When you are working with the known population parameters, the mean of the whole group and the standard deviation of the whole group you use the z-score. One of the more common examples is the mean and standard deviation of all GRE test takers. This groups has several million people in it, but we do know the mean and standard deviation. IQ scores are another example.

In practice we rarely know what the mean and standard deviation are of the whole group and instead rely on sample statistics to estimate the unknown parameters, you would then normally use the t-score. However, as the sample size increases, usually above around 30, the t-score and the z-score begin to get closer and closer to each other (a difference of less than a percent). As the sample size continues to increase the t becomes the z-score (when we get to the population size or infinity). A reasonable and conservative strategy is to use the t-score since it will mirror the z-score as your sample size increases.

Finally, there is another use of the term z-score, which is synonymous with standardized value. If you just want to standardize the values in a data-set, by subtracting each value from the mean and dividing that result by the standard deviation, you've created a z-score.