In a random sample of
six
people, the mean driving distance to work was
25.7
miles and the standard deviation was
6.7
miles. Assuming the population is normally distributed and using the t-distribution, a
99
%
confidence interval for the population mean
mu
is
left parenthesis 14.7 comma 36.7 right parenthesis
(and the margin of error is
11.0
).
Through research, it has been found that the population standard deviation of driving distances to work is
5.5
.
Using the standard normal distribution with the appropriate calculations for a standard deviation that is known, find the margin of error and construct a
99
%
confidence interval for the population mean
mu
.
Interpret and compare the results.