Question

Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 11 with a mean of 47.5 and a standard deviation of 12.7 at a confidence level of 99%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =

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

Answer 1

solution

Given that,

s =12.7

n = 11

Degrees of freedom = df = n - 1 =11 - 1 = 10

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df= t0.005,10 = 3.169 ( using student t table)

Margin of error = ME = t/2,df * (s /n)

=3.169 * (12.7 / 11)

ME= 12.1347

Margin of error = ME =12.1