t-scores versus z-scores (College Board AP® Statistics): Revision Note

t-scores versus z-scores

How do I know when to use a t-score or a z-score?

• It is important to be able to recognise which critical value to use for the inference test that you are conducting

  • You will need to consider the population distribution, the population parameters given and the sample size

What happens if the population is normally distributed?

• If a population is normally distributed and the population variance is known

  • then you should use a z-score

• If a population is normally distributed but the population variance is unknown

  • then you should use a t-score when the sample size is small,

• In practice, if the population variance is unknown but the sample size is large,

  • t-scores can be used

  • but z-scores can also be used

    • especially as the t-scores in the table run out for high values of n

  • If a z-score is used, then the sample standard deviation, , is used in place of the population standard deviation,

What happens if the population is not normally distributed?

• If a population is not normally distributed but

  • then, due to the Central Limit theorem, you can use z-scores

  • Use the population standard deviation, , if it is given

    • or the sample standard deviation, , if is not given

• If a population is not normally distributed and

  • then there is no statistical procedure you can use!