Question 1151773: The following random sample was selected : 4, 6, 3, 5, 9, 3. Find the 95% confidence interval for the mean of the population. See Ex. 2 (Use your graphing calculator to find the mean and sample standard deviation.)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
mu = population mean
sample = {4,6,3,5,9,3}
n = 6 is the sample size
use a calculator to find that
xbar = 5 is the sample mean
s = 2.280 is the approximate sample standard deviation
At 95% confidence, the critical z value is approximately z = 1.960
Use a table like this to find the proper critical value
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
(look at the value in the bottom row just above the 95% confidence level)
L = lower boundary of confidence interval
L = xbar - z*s/sqrt(n)
L = 5 - 1.960*2.280/sqrt(6)
L = 5 - 1.824
L = 3.176
L = 3.18
U = upper boundary of confidence interval
U = xbar + z*s/sqrt(n)
U = 5 + 1.960*2.280/sqrt(6)
U = 5 + 1.824
U = 6.824
U = 6.82
The 95% confidence interval is (L, U) = (3.18, 6.82)
Which can also be expressed as 3.18 < mu < 6.82
The second version of the answer is in the form L < mu < U.
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