Question

Construct the confidence interval for the population mean mu. cequals0.98​, x overbar equals 16.9​, sigmaequals9.0​, and nequals50 A 98​% confidence interval for mu is left parenthesis nothing comma nothing right parenthesis . ​(Round to one decimal place as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 16.9

Population standard deviation = = 9.0

Sample size = n = 50

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01= 2.326

Margin of error = E = Z_/2* ( /n)

= 2.326 * ( 9.0/ 50)

= 3.0

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

- E < < + E

16.9 - 3.0 < < 16.9 + 3.0

13.9 < < 19.9

(13.9 , 19.9)