We use a t distribution for inference about a population mean instead of the standard Normal distribution:

a. if the original population does not have a Normal distribution.
b. if we do not have a simple random sample.
c. if we do not know the population standard deviation and must use the sample standard deviation.
d. if we do not know the population mean and must use the sample mean.

(c) If we do not know the population standard deviation and must use the sample standard deviation

Explanation:

A t distribution is used for the inference about the population mean if the population standard deviation (sigma) is unknown. The sample standard deviation (s) is used instead.

The test statistic of a t distribution is given as (sample mean - population mean) ÷ (sample standard deviation ÷ sqrt(sample size))

The test statistic of a standard normal distribution is given as (sample mean - population mean) ÷ (population standard deviation ÷ sqrt(sample size))

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