Question 1182052: a. A random sample of size 81 is taken from a large population, measuring the time it takes to complete a driver’s license examination. The sample mean was found to be 43 minutes, and the sample standard deviation 5.71 minutes. Construct a 95% confidence interval around the sample mean. Be sure to show whether you use the t- or z- value, and what value you use. Please use the exact value appropriate for these circumstances (rather than the approximations sometimes referred to as the empirical rule). Interpret the confidence interval in a single sentence. In another sentence, state why you used either the “t” or the “z”.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! We don't know the sd of the population, only that it is large (and probably normal).
This means we will use a t-test
half-interval for 95%CI is t (0.975,df=80)*s/sqrt(n)
=1.99*5.71/9
=1.26
the interval is (41.74, 44.26) min
We don't know the exact mean of the population, but we are highly (95%) confident it lies in the interval shown.
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