The snout vent lengths (in centimeters) in 20 newly born garter snakes selected at random from several litters are given below. Compute the 95% and the 99% confidence intervals for the population mean.

6.5, 6.2, 4.9, 5.1, 4.3, 5.8, 5.0, 5.4, 4.6, 5.4, 4.7, 4.8, 6.0, 5.2, 3.4, 3.8, 4.7, 4.8, 3.9, and 6.1

So far what I did was get the mean and standard deviation from the data given above.

Mean = ( Σ xi ) / n = 100.6 / 20 = 5.03

Standard deviation = sqrt[ (1/n) * Σ (xi - mean)^2 ] = sqrt[ (1/20) * 13.022 ] = 0.807

I'm not sure if I am solving this correctly or not. Please help?