Question 1183039: The 90% confidence interval for the mean one way commuting time in New York is {5.22 and 5.98 minutes}. Construct a 95% confidence interval based on the same data. Which interval provide more information. Please can you help me solve this question?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The mean is in the center or 5.60 min
the 90% half-interval is z(0.95)*sigma/sqrt(n)
=1.645 sigma/sqrt(n)
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The 95% half-interval is 1.96 sigma/sqrt(n)
It will be larger based on the ratio of 1.96/1.645 applied to the above, since everything else is identical.The ratio is 1.19.
The half-interval will be 1.19 times larger or 0.45 minutes
(5.15, 6.05) min
For something like commuting time which is small in this instance, the 95% CI gives essentially the same information as the 90% CI with the advantage of higher confidence. It would be a different matter if we had to raise the sample size to get a similar interval width, which is what usually has to be done. But most aren't going to see the two intervals as very different and will say it is somewhere around 5-6 minutes.
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