SOLUTION: A sample of 230 observations is selected from a normal population for which the population standard deviation is known to be 26. The sample mean is 18. a. Determine the stand

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Question 1058592: A sample of 230 observations is selected from a normal population for which the population standard deviation is known to be 26. The sample mean is 18.

a.
Determine the standard error of the mean. (Round your answer to 3 decimal places.)

Standard error of the mean:

b.
Determine the 99% confidence interval for the population mean. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

Confidence interval between and

Found 2 solutions by hussamuddin, Boreal:
Answer by hussamuddin(51) (Show Source):
You can put this solution on YOUR website!
not clear

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
The SEM is sigma/sqrt(n)=26/sqrt(230)=1.714
That means that although the mean of the sampling distribution is the same, the SD is much less. It is very unlikely all of the 230 observations will be 1 SD to one side or the other of the mean.
The 99% CI uses z=2.576
z*SEM is the interval width is 4.415
(21.585,30.415)