Question

If Upper X overbarequals 113​, sigmaequals 22​, and nequals 38​, construct a 99​% confidence interval estimate of the population​ mean, mu .

The 99​% confidence interval is nothing less than or equals mu less than or equals nothing. ​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 113

Population standard deviation =    = 22

Sample size = n = 38

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 * ( 22 /   38 )

= 9.19

At 90% confidence interval estimate of the population mean is,

- E < < + E

113 - 9.19 <   < 113 + 9.19

103.81 <   < 122.19

( 103.81 ; 122.19 )