Question

Salaries of 42 42 college graduates who took a statistics course in college have a​ mean, x overbar x​, of $ 68 comma 000 $68,000. Assuming a standard​ deviation, sigma σ​, of ​$ 13 comma 437 13,437​, construct a 90 90​% confidence interval for estimating the population mean mu μ.

Answer 1

Solution :

Given that,

= 68000

= 13437

n = 42

At

90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645* ( 13437/ 42)

= 3410.7

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

- E < < + E

68000-3410.7 < < 68000+3410.7

64589.3< < 71410.7

(64589.3, 71410.7)