Question

I have draw a random sample of 20 of my neighbors. I ask them their income (What can I say? I'm a nosy neighbor). My sample average (x bar) is $41,000. I want to create a 95% confidence interval around x bar.

My estimated standard deviation is $5,000.

What is the 95% confidence internal for the average income in my neighborhood? $38,652 to $43.347, $38,663 to $43,336, $38,809 to $43,191, or not enough information?

Answer 1

Solution :

Given that,

= $41000

=$5000

n = 20

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 * ( 5000 /  20 )

= 2191

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

- E < < + E

41000- 2191 <   < 41000+ 2191

38809 <   <43191

( $38,809 to $43,191 )