PLEASE SHOW CALCULATOR STEPS The housing market has recovered slowly from the ec

Question

PLEASE SHOW CALCULATOR STEPS

The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 30 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was $9810 with a standard deviation of $121. In 2011, the average home in this region of the country lost $9253 in value. Was the community studied by the realtors unusual? Use a t-test to decide if the average loss observed was significantly different from the regional average with 0.05 as theP-value cutoff level.

a) State the hypothesis

b) Calculate the test statistic

c) Calculate the P-value

d) State the conclusion

(again, please list steps using TI-84 Plus calculator)

Explanation / Answer

t-test For Single Mean
Set Up Hypothesis
Null, H0: U=9523
Alternate, H1: U!=9523
Test Statistic
Population Mean(U)=9523
Sample X(Mean)=9810
Standard Deviation(S.D)=121
Number (n)=30
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =9810-9523/(121/Sqrt(30))
to =12.991
| to | =12.991
Critical Value
The Value of |t | with n-1 = 29 d.f is 2.045
We got |to| =12.991 & | t | =2.045
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 12.9914 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho

average loss observed was significantly different from the regional average

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