Find the margin of error M.E. that corresponds to a sample of size 16 with a mean of 50.3 and a standard deviation of 9.6 at a confidence level of 99.5%.

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 16 with a mean of 50.3 and a standard deviation of 9.6 at a confidence level of 99.5%. Report ME accurately to one decimal place because the sample statistics are presented with this accuracy. 

 

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

since population standard deviation is not known (and sample size is less than 30), we would use the t distribution in the computation of the margin of error.

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

SD is given as 9.6 and sample size given as 16

for 99.5% confidence level, alpha = 0.5% = 0.005.

critical t value would be t for alpha/2 = 0.0025 and sample size - 1 = 15 degrees of freedom = 3.286