Question

A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 114 homeowners selected from this area showed that they pay an average of $1579 per month for their mortgages. The population standard deviation of such mortgages is $213.

Find a 95% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area.

Round your answers to two decimal places.

____to____  dollars

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $1579

Population standard deviation =    = $213

Sample size n =114

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* ( 213 /  114 )

E= 39.10
At 95% confidence interval estimate of the population mean
is,

- E < < + E

1579 - 39.10 <   < 1579 + 39.10

1539.90 <   < 1618.10

( 1539.90 , 1618.10)