Question

Salaries of 42 college graduates who took a statistics course in college have a​ mean, x overbar​, of $ 68,500. Assuming a standard​ deviation, σ, of ​$13,898​, construct a 99​% confidence interval for estimating the population mean μ.

​$___< μ <​ $ ___

​(Round to the nearest integer as​ needed.)

Answer 1

Given that,

= 68500

= 13898

n = 42

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

=2.576 * (13898 / 42)

= 5524

At 99% confidence interval estimate of the population mean is,

- E < < + E

13898 - 5524 < < 13898 + 5524

8374< < 19422

(8374, 19422)