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.

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- Apr 6th 2007, 10:28 PMharryNormal Distribution
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.

- Apr 6th 2007, 11:01 PMCaptainBlack
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