Question

Construct the confidence interval for the population mean mu. cequals0.98​, x overbar equals 4.2​, sigmaequals0.6​, and...

Construct the confidence interval for the population mean mu. cequals0.98​, x overbar equals 4.2​, sigmaequals0.6​, and nequals43 A 98​% confidence interval for mu is (Round to two decimal places as needed)

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Answer #1

Solution :

Given that,

Point estimate = sample mean = \bar x = 4.2

Population standard deviation =   \sigma = 0.6

Sample size = n =43

At 98% confidence level the z is ,

\alpha = 1 - 98% = 1 - 0.98 = 0.02

\alpha / 2 = 0.02 / 2 = 0.01

Z\alpha/2 = Z0.01 = 2.326


Margin of error = E = Z\alpha/2 * ( \sigma /\sqrtn)

= 2.326 * ( 0.6/  \sqrt43 )

= 0.21
At 98% confidence interval estimate of the population mean
is,

\bar x - E < \mu < \bar x + E

4.2​ - 0.21<  \mu < 4.2​ + 0.21

3.99 <  \mu < 4.41

( 3.99 , 4.41 )

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