Question

From a normally distributed population, a simple random sample of size 30 is taken. The mean of the sample is 144 and the standard deviation of the sample is 12.
Which interval is the 90% confidence interval for the population mean?

(139.7, 148.3)
142.4, 145.6)
143.3, 144.7)
140.4, 147.6)

Answer 1

Answer: Choice D
The 90% confidence interval for the population mean mu is (140.4, 147.6)

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Work Shown:

xbar = 144 (sample mean)
s = 12 (sample standard deviation)
n = 30 (sample size)
z = 1.645 (critical value at 90% confidence; use a calculator or table to compute this value)

The lower limit of the confidence interval is L, which is found by
L = xbar - z(s/sqrt(n))
L = 144 - 1.645(12/sqrt(30))
L = 140.395985571616
L = 140.4

Similarly the upper limit U is
U = xbar + z(s/sqrt(n))
U = 144 + 1.645(12/sqrt(30))
U = 147.604014428384
U = 147.6

The 90% confidence interval is therefore (L,U) = (140.4, 147.6)