According to a recent survey, a random sample of 100 homes sold in the Baton Rouge...

According to a recent survey, a random sample of 100 homes sold in the Baton Rouge metro area had an average sale price of $263,000. If the population standard deviation of home prices is $20,000, what is the 99% confidence interval of the true population average sales price for homes sold in Baton Rouge?

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Expert Solution

Solution :

Given that,

Point estimate = sample mean = = $263000

Population standard deviation = = $20000
Sample size = n =100

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

=2.576 * ( 20000/ $\sqrt$ 100)

= 5152

At 99% confidence interval estimate of the population mean is,

- E < < + E

263000- 5152< <263000+ 5152

257848< < 268152

(257848, 268152)

orchestra answered 1 year ago

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