Question

The housing market has recovered slowly from the economic crisis of 2008.​ Recently, in one large​ community, realtors randomly sampled 32 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was ​$8251 with a standard deviation of ​$1739 .Find a 90​% confidence interval for the mean loss in value per home. ​Answer should be= ($__, $__)

Answer 1

Solution:

Given that,

n = 32

= 8251   

s = 1739

Note that, Population standard deviation() is unknown..So we use t distribution.

Our aim is to construct 90% confidence interval.   

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05

Also, d.f = n - 1 = 32 - 1 = 31

    =    =  _0.05,31 = 1.700

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.700 * (1739  / 32)

= 522.6049

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(8251   - 522.6049)   <   <  (8251  + 522.6049)

7728.3951 <   <  8773.6049

Required 90% confidence interval is

($ 7728.3951 , $ 8773.6049)