Question

Assume that a sample is used to estimate a population proportion μμ. Find the margin of error M.E. that corresponds to a sample of size 41 with a mean of 50.2 and a standard deviation of 12.9 at a confidence level of 95%.

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,

Point estimate = sample mean = = 50.2

Population standard deviation =    = 12.9

Sample size = n = 41

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = M.E = Z/2 * ( /n)

= 1.960 * ( 12.9 /  41 )

= 3.9

Margin of error = M.E = 3.9