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 23 with a mean of 74.6 and a standard deviation of 6.8 at a confidence level of 99.5%.

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:

Sample size = n = 23

Sample mean = 74.6

Sample standard deviation = s = 6.8

confidence level = c = 99.5%

We have to find margin of Error M.E.

where t_c is t critical value for c = 99.5% confidence level and df = n - 1 = 23 - 1 = 22

Thus two tail area = 1 - c = 1 - 0.995 = 0.005

Since t table do not include two tail area = 0.005 or 99.5% confidence level , we need to use Excel to find t critical value.

( let me know if you are using other technology)

=T.INV.2T( probability , df )

=T.INV.2T( 0.005, 22 )

=3.119

Thus t_c = 3.119

Thus