An engineer is interested in estimating the population mean using a random sampl
ID: 2924813 • Letter: A
Question
An engineer is interested in estimating the population mean using a random
sample of n=64 observations. The sample has the mean of 1.5 and the variance of 4.0. Based on this
data, the engineer has obtained the following confidence interval for the population mean:
(0.85625, 2.14375)
a) What is the value of that was used for the construction of the above confidence interval? Explain.
b) Find the 95% confidence interval constructed using the same random sample? Is this confidence
interval narrower or wider than the interval above? Why?
c) If the engineer wants to reduce the width of the confidence interval without changing the value of ,
what would you recommend?
Explanation / Answer
n= 64 observations ; standard deviation = sqrt(4) = 2.0
(a) For the given confidence interval
Lower value LCL = - Za (s/ sqrt(n)
0.85625 = 1.5 - Za (2/ sqrt(64))
0.85625 = 1.5 - Za *0.25
Za = 2.575
That means p - value for one side from Z - table = +- 0.005
so confidence interval = 99% CI
(b) 95 % CI = +- Z95% (s/ sqrt(n)
95% CI = 1.5 +- 1.96 * (2/ sqrt(64)
= 1.5 +- 1.96 * (1/4)
= (1.01, 1.99)
The confidence interval is narrower than the interval above.
(c) If engineer wants to reduce the width of the confidence interval without changing the value of alpha, we would increase the sample size.