Question 1120011: a) A consumer agency that proposes that lawyers’ rates in a particular city are too high wanted to
estimate the mean hourly rate for all lawyers in that city. A sample of 70 lawyers taken from the
city showed that the mean hourly rate charged by them is $420. The population standard deviation
of hourly charges for all lawyers is $110.
i. Construct a 95% confidence interval for the mean hourly charges for all lawyers in the City.
ii. Briefly interpret the interval constructed in a) (i) above.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The half interval is z*sigma/sqrt (n)
This is 1.96*110/sqrt(70) for a 95% CI
=$25.77
interval is $420+/- $25.77
($394.23, $445.77)
This means while we don't know the exact mean, short of surveying every lawyer, we can be very confident that the true value lies in this interval. We are using confidence, because the true value either DOES or DOES NOT lie in the interval, and that is not a useful probability statement.
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