A random sample of the duration of 50 telphone calls handled by a local telephone company had a mean of 11.6 min and a standard devation of 3.8 Minutes. Find a 95% confidence interval for the true mean duration of calls handled by the company.
A random sample of the duration of 50 telphone calls handled by a local telephone company had a mean of 11.6 min and a standard devation of 3.8 Minutes. Find a 95% confidence interval for the true mean duration of calls handled by the company.
The random variable:
t = (SampleMean - PopulationMean)/(SampleSD/sqrt(n))
where n is the sample size, has a t distribution
With n=50, nu the number of degrees of freedom is 49, with this number of
degrees of freedom a 95% interval for t is ~=(-2.01, 2.01). So the 95%
confidence interval for the populaion mean is:
(SampleMean - 2.01*SampleSD/sqrt(n), SampleMean + 2.01*SampleSD/sqrt(n))
or: (10.52, 12.68).
If you used the normal approximation here the 2.01 would be replaced by 1.95
and the interval would be (10.55, 12.65)
RonL