Question

Salaries of 44 college graduates who took a statistics course in college have a​ mean, x overbar​, of $67,600. Assuming a standard​ deviation, sigma​, of ​$19,598​, construct a 90​% confidence interval for estimating the population mean

$___< u<$_____

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 67600

Population standard deviation = =19598

Sample size = n = 44

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z0.05 = 1.645

Z/2 = 1.645  
Margin of error = E = Z/2 * ( /n)

=1.645 * ( 19598 /  44 )

= 4859.74

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

- E < < + E

67600 - 4859.74 <   < 67600 + 4859.74

62740.26 <   <72459.74.

(62740.26 ,72459.74. )