The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 39 for a sample of size 19 and standard deviation 8.
Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level).
Give your answers to one decimal place and provide the point estimate with its margin of error.
I began by finding the upper an lower bounds. $\Rightarrow 39 \pm \dfrac{8}{\sqrt{19}}$ $= 34.340$ and $43.660$
Then I went on to find the point estimate: $p=(34.340+43.660)/2=39$ but $p=X/n$ $\Rightarrow X= 19 \cdot 39=741$.
I put this in and the computer says I'm wrong.
My margin of error is $4.7$ (which is correct).
The standard deviation is the sample SD. And the formula she gave is of the form $x_{mean} ± t_{\alpha/2} \cdot s/\sqrt{2}$. Using t-table. What am I doing wrong?