Question

Salaries of 35 college graduates who took a statistics course in college have a​ mean, x overbar​, of $ 64 comma 500. Assuming a standard​ deviation, sigma​, of ​$10 comma 141​, construct a 99​% confidence interval for estimating the population mean mu.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 64500

Population standard deviation =    = 10141
Sample size = n =35

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576* (10141 / 35)

= 4416

At 99% confidence interval estimate mean is,

- E < < + E

64500 -4416< < 64500+4416

60084< < 68916