Question

This is under "Confidence Intervals for a Mean":

Assume that a sample is used to estimate a population mean μ. Find the margin of error M.E. that corresponds to a sample of size 12 with a mean of 46.8 and a standard deviation of 13.2 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

Solution :

Given that,

Point estimate = sample mean = = 46.8

Population standard deviation =    = 13.2

Sample size = n =12

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 * (13.2 / 12 )

= 6.268