Confidence Interval for Mean

Build a normal-approximation confidence interval for the mean of a sample: $\bar{x}\pm z\cdot s\mathrm{/}\sqrt{n}\backslash bar\; x\backslash pm\; z\backslash cdot\; s/\backslash sqrt\; n$ with the unbiased standard deviation $ss$ and a critical value critical (default $1.961.96$, i.e. 95%).

Implement solve(x, critical=1.96).

Returns. Return a tuple (low, high). The sample needs at least two values so that $ss$ exists.

Examples

Example 1

Input:

solve([1.0, 2.0, 3.0, 4.0])

Output:

(1.234825, 3.765175)

Example 2

Input:

solve([10.0, 12.0, 11.0, 13.0, 9.0], critical=2.576)

Output:

(9.178493, 12.821507)