Based on the data given, we have a small size as a sample since n = 11.
Other given data are the mean = 58, sample SD = 17.9, and a population mean of 81.2. With a sample size small and unknown population standard deviation, the test statistic appropriate for this would be t-test. The formula is:
[tex]t=\frac{\bar{x}\text{ }-\mu}{\frac{s}{\sqrt[]{n}}}[/tex]
Knowing the data given above, let's apply it to the formula.
[tex]t=\frac{58-81.2}{\frac{17.9}{\sqrt[]{11}}}=\frac{-23.2}{5.39705}\approx-4.299[/tex]
The test statistic is -4.299 and a p-value of 0.0008. (one-tail)
