Question 1192337: A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 214 milligrams with s = 11.8 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content, µ, of all such eggs.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
µ = greek letter mu = population mean
n = 82 = sample size
xbar = 214 = sample mean
s = 11.8 = sample standard deviation
Even though we don't know sigma (the population standard deviation), we can use the Z distribution because n ≥ 30.
At 95% confidence, the z critical value is roughly z = 1.96 in which you use a table or calculator to find this value.
It's used fairly often in statistics that I recommend memorizing it, but having a reference table is the next best thing.
The margin of error is
E = z*s/sqrt(n)
E = 1.96*11.8/sqrt(82)
E = 2.554060 approximately
The lower bound is
U = xbar - E
U = 214 - 2.554060
U = 211.44594
U = 211.45
The upper bound is
U = xbar + E
U = 214 + 2.554060
U = 216.55406
U = 216.55
The 95% confidence interval is approximately (211.45, 216.55) which is in the format (L, U).
If you wish to write the answer in the format L < mu < U, then you'd write 211.45 < mu < 216.55
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