Some company manufactures printers. You have been asked to construct a confidenc

Question

Some company manufactures printers. You have been asked to construct a confidence interval (CIE) that can be used to estimate the population mean life. You take a random sample of 81 printers and find the sample mean life to be 8.50 years with a sample standard deviation of 2.70 years. Construct the following confidence interval estimators (CIE). You may use the sample standard deviation as the population s.d. and assume X is normal since the sample size is quite large. (1). Construct an 80% CIE (2). Construct an 99% CIE.

Explanation / Answer

The CIE is given by Mean +/- Z*s/sqrt(n) , where:

n = sample size = 81

Mean = Sample mean

s = Sample stdev

Therefore,

a. 80% CIE is given by :

Z = 1.28

So, CIE @ 80%: 8.50 +/- 1.28*2.7/sqrt(81)

= 8.116 to 8.884

b. 99% CIE is :

8.50 +/- 2.56*2.7/sqrt(81)

=7.732 to 9.268

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