# Z or T

“The average return on small stocks over the period 1926-1997 was 17.7%, and the standard error of the sample was 33.9%. The 95% confidence interval for the return on small stocks in any given year is” Which should I use : a Z-statistic or T-statistic ?

The rule of thumb is to use a Z statistic if N > 30. Otherwise use the T statistics.

The T-statistics will be used since you were given the ‘standard error of the sample’. You would have used the Z-statistic if the standard error was the ‘standard error of the population’

Thanks for the clarification…

I don’t think that’s correct. The two key questions to ask when deciding between Z-stat or T-stat are: 1) Is the distribution normal or non-normal? 2) Is the variance known or unknown? If n is > 30, then you can always use the Z-stat (though the T-stat would be more conservative when variance is unknown). If the distribution is non-normal and n is < 30 then you cannot use either the T-stat or Z-stat. For this question, I would use the Z-stat since n=72.