find a 99% confidence interval given ∑_i=1⁶¹ X_i = 6450 and ∑_i=1⁶¹ X^2_i = 6450

Question

find a 99% confidence interval for the mean given:

∑_i=1⁶¹ X_i = 6450

and

∑_i=1⁶¹ X^2_i = 6450

I found the sample mean of 105.7377 . (6450/61)

I do not know how to find the variance. Then confidence interval is computable.

Answer 1

CI for mean or which? You can use those formulas to find the sample variance too.

$s^{2}= \frac{\sum_{i=0}^n x^{2}_{i} - (\sum_{i=0}^n x_{i})^{2}/n}{n-1} $

If for mean you will use a T-interval

$(\bar{x} - t_{\alpha/2,df}{\frac{s}{\sqrt{n}}},\bar{x} + t_{\alpha/2,df}{\frac{s}{\sqrt{n}}}) $

where df=n-1