Question

Salaries of 47 college graduates who took a statistics course in college have a​ mean, overbar x​, of $65,600. Assuming a standard​ deviation, σ​, of $12,213​, construct a 95​% confidence interval for estimating the population mean μ.

$__ < μ < $ __

Answer 1

Solution :

Given that,

Point estimate = sample mean =     =65600

Population standard deviation =    = 12213

Sample size n =47

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 * (12213 / 47 )

E= 3491.6403
At 95% confidence interval estimate of the population mean
is,

- E < < + E

65600 -3491.6403 <   <65600 + 3491.6403

62108.3597 <   < 69091.6403

( $ 62108.3597 <   < $69091.6403)