Question

Construct the confidence interval for the population mean

muμ.

cequals=0.980.98​,

x overbar equals 8.2x=8.2​,

sigmaσequals=0.90.9​,

and

nequals=5858

A

9898​%

confidence interval for

muμ

is

left parenthesis nothing comma nothing right parenthesis .,.

​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 8.2

Population standard deviation =    = 0.9

Sample size = n =58

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 ( see the 0.01 value in standard normal (z) table corresponding z value is 2.326 )

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

= 2.326 * ( 0.9 /   58)

E=0.27
At 98% confidence interval estimate of the population mean
is,

- E < < + E

8.2 - 0.27   <   < 8.2 + 0.27

7.93 <   < 8.47

(7.93 , 8.47)