Single Mean

The population standard deviation is known.

The standard error of the mean is $2.5$. You then find the probability of a sample mean more than $25-20=5$ from the population mean of $20$. This is the probability outside $15$ and $25$ given a distribution with a mean of $20$ and a standard deviation of $2.5$. The probability is .0455.

$2.6693$ Make sure you divide by $\mathrm{N}-1$.

$0.9437$ You divide $s$ by the square root of $\mathrm{N}$.

You divide $\mathrm{M}=1.625$ by the standard error of the mean $(.9437)$ to get $1.72$.

You use $N-1=7$ degrees of freedom. $p=.1288$

$t=1.4626$

$t=-0.7917$

$p=0.8319$