Question

Construct the confidence interval for the population mean mu . cequals 0.98​, x overbar equals 8.3 ​, sigma equals0.7​, and nequals 50 A 98 ​% confidence interval for mu is left parenthesis nothing comma nothing right parenthesis . ​(Round to two decimal places as​ needed.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 8.3

Population standard deviation =    = 0.7

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 ( Using z table    )

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

= 2.326 * ( 0.7 /  50 )

E= 0.23
At 98% confidence interval estimate of the population mean
is,

- E < < + E

8.3 - 0.23 <   < 8.3 + 0.23
8.07<   < 8.53

( 8.07, 8.53 )