# How to perform Student's t-test having only sample size, sample average and population average are known?

Student's $t$-test requires the sample standard deviation $s$. However, how do I compute for $s$ when only the sample size and sample average are known?

For example, if sample size is $49$ and sample average is $112$, I will then attempt to create a list of $49$ identical samples with values of $112$ each. Expectedly, the sample standard deviation is $0$. This will create a divide-by-zero problem in the $t$ test.

The average income of ACME North Factory workers is $\$200$. It is reported that a random sample of$49$workers in ACME South Factory had an annual income of$\$112$. Is this difference statistically significant?