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?
Am I correct in saying that the population mean is $\$200$?