Question

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 $30,000, what is the 90% confidence interval of the true population average sales price for homes sold in Baton Rouge?

Select one:

(258065, 267935)

(259160, 266840)

(255275, 270725)

(257120, 268880)

none of these are correct

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 263,000

Population standard deviation =    = 30,000
Sample size = n =100

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645 * ( 30,000/   100)

= 4935
At 90% confidence interval mean
is,

- E < < + E

263,000 - 4935 <   < 263,000 + 4935

258065 <   <  267935

(258065, 267935)