Question

The average price for new mobile homes is known to be distributed with population standard deviation of 300. If a random sample of 36 homes resulted in a sample mean of 55, 000, obtain a 90% confidence interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 55000

Population standard deviation = = 300

Sample size = n = 36

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z_0.05 = 1.645

Z/2 = 1.645

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

= 1.645* ( 300 /  36 )

= 82.24

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

- E < < + E

55000 - 82.24 <   < 55000 + 82.24

54917.76 <   < 55082.24

( 54917.76 ,55082.24 )