A random sample (normal distribution) of $20$ items is drawn from a population that is known to be normally distributed. The sample has a mean of $60$ and a standard deviation of $16$. Test the hypothesis that the true mean of the population from which the sample is taken is $68$.
My calculations:
Find std error of mean = $\dfrac{16}{\sqrt{20}}\approx 3.58$
Therefore, the population mean is very likely to be between 7.16-10.73 of 60 Is my conclusion correct? Did i set this up correctly?