Question

The housing market has recovered slowly from the economic crisis of 2008.​ Recently, in one large​ community, realtors randomly sampled 29 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was ​$9440 with a standard deviation of ​$2030. In​ 2011, the average home in this region of the country lost ​$8874 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 the​ P-value cutoff level.

Answer 1

Answer: Let us construct the null and alternative hypotheses as H0: mu = 8874 vs Ha: mu not equal to 8874.

Where mu is the unknown average loss in the population of home value.

The test statistic used to test this hypothesis is T = (xbar - mu0)/(s/sqrt(n)), where xbar is the sample mean, s = sample standard deviation, mu0 is the hypothesized value of the unknown population mean and n is the sample size. sqrt refers to the square root function.

We reject H0 if |T(observed)| > t(alpha/2,(n-1)), where t(alpha/2,(n-1)) is the upper (alpha/2) point of the Student's t distribution with (n-1) degrees of freedom. Alpha is the level of significance.

Here T(observed) = 1.501479 and t(alpha/2,(n-1)) = 2.048407. Thus we see that |T(observed)| < t(alpha/2,(n-1)). Thus we fail to reject H0 and conclude on the basis of the given sample measures at a 5% level of significance that the average loss observed was not significantly different from the regional average.

[The answers are obtained using R-software. The code and output are attached below.]