I am kind of new in calculation of confidence interval, so I hope it will not be a too basic question.
I have a normal distribution (with slightly longer left tail) as you can see in the picture. The sample size is 2286 and I am trying to calculate the level of 99% CI (confidence interval) with the formula below:
x_bar is the mean value of the sampled data which is around 7.57,
t_star is the confidence coefficient from the t-table which is 2.576 because of the size of the sample data,
s is estimated standard deviation which is around 1.71 (the standard deviation value is generated in SAS-program with
and n is the sample size which is 2286 as mentioned above.
So the formula gives the upper limit as 7.66 with 99% confidence intervall. However, according to the histogram like below, I should get a value around 11.
What am I doing wrong?