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 13 with a mean of 32.6 and a standard deviation of 16.2 at a confidence level of 90%.

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

Given that,

= 32.6

s =16.2

n = 13

Degrees of freedom = df = n - 1 =13 - 1 = 12

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,12 = 1.782    ( using student t table)

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

= 1.782 * (16.2 / 13) = 8.0066

Margin of error = E = 8.0