It looks like you are fine so far.
Just convert 95% and 99% into the number of standard deviations about the mean and apply that to the mean.
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?