Confidence Intervals for the Mean

Question

Assume that a sample is used to estimate a population mean . Find the margin of error M.E. that corresponds to a sample of size 8 with a mean of 57.8 and a standard deviation of 13.7 at a confidence level of 99.5%.Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.

M.E. = 

Answer 1

margin of error = t-critical value * standard deviation/square root(sample size)

t-critical value for 99.5% CI and degrees of freedom = sample size - 1 = 7.

Look at tail probability of 0.0025 (which corresponds to 99.5% CI) and 7 DOF. t-critical = 4.029

margin of error = 4.029 * 13.7/(sqrt(8) = 19.5