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five_am_grind2026-05-21
cfaLevel IQuantitative MethodsHypothesis Testing

When should I use a t-test instead of a z-test for a one-mean CFA question?

I understand the numerator is sample mean minus hypothesized mean, but I keep mixing up the reference distribution. What clue tells me to use t?

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Use a t-test when the population standard deviation is unknown and the prompt uses the sample standard deviation to estimate the standard error. That is the common exam setup because real analysts usually do not know the true population standard deviation.

Suppose a sample of 25 monthly active returns has a mean of 0.42 percent and a sample standard deviation of 1.10 percent. If the null mean is 0.00 percent, the statistic uses 1.10 / square root of 25 in the denominator and is evaluated against a t distribution with 24 degrees of freedom. A z-test would require a known population standard deviation or an explicit instruction to use the normal distribution.

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