Question

10. After sampling 16 members of a normal population you find the sample mean equals 20 and the sample standard deviation, s, equals 4. Construct a 90% confidence interval estimate for μ.

a. 18.04-21.96
b. 18.25-21.75
c. 18.36-21.64
d. None of the above

Answer 1

c. 18.36-21.64

Explanation:

Using the following formulas the lower and upper limits of the interval are calculated

Lower limit = mean - (standard deviation /√sample size)* Zr

Upper limit = mean + (standard deviation /√sample size)* Zr

Zr depends on confidence interval

Zr for 90% = 1.645

then

Lower limit = 20 - (4 /√16)* 1.645 = 18.355 ≈ 18.36

Upper limit = 20 + (4 /√16)* 1.645 = 21.645 ≈ 21.64