Question

Salaries of 33 college graduates who took a statistics course in college have a​ mean, x overbar x​, of $67,700. Assuming a standard​ deviation, sigma σ​, of ​$10,608​, construct a 95​% confidence interval for estimating the population mean μ.

Answer 1

Solution :

Given that,

= 67700

=10608

n = 33

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96* (10608 / 33)

= 3619.37 (rounded)

At 95% confidence interval estimate of the population mean is,

- E < < + E

67700-3619.37 < <67700+3619.37

64080.63< < 7131.37

(,64080.63, 7131.37 )