Question

The average price for new mobile homes is known to be distributed with a 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 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 * (300 /  36 )

= 82.2500
At 90% confidence interval estimate of the population mean
is,

- E < < + E

55000 - 82.2500 <   < 55000+ 82.2500

57917.7500 <   < 55082.2500

( 57917.7500 , 55082.2500, )