SOLUTION: A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 3. The sample mean is 23. (Round your answers to 3 decim

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Question 922869: A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 3. The sample mean is 23. (Round your answers to 3 decimal places.)

(a) The standard error of the mean is ....

(c)
The 99 percent confidence interval for the population mean is between ... and ....

I have already solved (a) and the standard error of the mean is .948 but I am having trouble with the confidence interval. Can you please show your work so I can understand how to work these types of problems?
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
mean = 23, sd(population) = 3
a) SE = sd/sqrt(n) = 3/sqrt(10) = .9487
b) 99% CI (see chart below)
ME = 3.25SE = 3.25(.9487) = 3.08 = 3
Round the confidence interval limits to the same number of decimal places as the sample mean
ME = 3
CI: 23-ME < u < 23 + ME
CI: (20, 26)
.......Small Samples
DF Probability, p 2-tailed
0.1 0.05 0.01 0.001
1 6.31 12.71 63.66 636.62
2 2.92 4.3 9.93 31.6
3 2.35 3.18 5.84 12.92
4 2.13 2.78 4.6 8.61
5 2.02 2.57 4.03 6.87
6 1.94 2.45 3.71 5.96
7 1.89 2.37 3.5 5.41
8 1.86 2.31 3.36 5.04
9 1.83 2.26 4.78
10 1.81 2.23 3.17 4.59
....Larger Samples
= CI z = value
90% z =1.645
92% z = 1.751
95% z = 1.96
98% z = 2.326
99% z = 2.576