Question

Salaries of 46 college graduates who took a statistics course in college have a​ mean, x overbarx​, of $ 67,000. Assuming a standard​ deviation, sigmaσ​, of ​$15,669​, construct a 90​% confidence interval for estimating the population mean muμ.

$_____ < μ < $________

(Round to the nearest integer as needed)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 67,000

Population standard deviation =    = 15,669​,

Sample size = n =46

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645* ( 15,669​ /  46 )

= 3800
At 90% confidence interval
is,

- E < < + E

67000 - 3800 <   67000 + 3800

$_63200____ < μ < $__70800______