Question

The housing market has recovered slowly from the economic crisis of 2008.​ Recently, in one large​ community, realtors randomly sampled

28 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was

​$8053 with a standard deviation of

​$1477.

In​ 2011, the average home in this region of the country lost

​$7750

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

$\mu$ :  the average loss

Null hypothesis : H_o : $\mu$ = 7750

Alternate Hypothesis : H_a: $\mu$ $\neq$ 7750

Two tailed test;

Hypothesized mean : regional average : $\mu _{o}$ = 7750

Number of randomly sampled bids: sample size : n= 28

sample average loss : $\overline{x}$ = 8053

sample standard deviation :s = 1477

- μo Test Statistic: tstat =- s/n

(8053 - 7750) 1477/28 303 279.1268 1000 = 1.0855

Value of test statistic = 1.0855

Degree of freedom = n-1 = 28-1 =27

For two tailed test:

P – Value = P(t < -tstat) + P(t > tstat) = 2 x P(t > 1.0855)

for 27 degrees of freedom,

P(t > 1.0855) = 0.1436

p-value = 2 x P(t>1.0855) = 2 x 0.1436 = 0.2872

p-value cutoff level = 0.05

As P-Value i.e. is greater 0.05 i.e (P-value:0.2873 > 0.05); Fail to Reject Null Hypothesis

There is not sufficient evidence to conclude that average loss observed was significantly different from the regional average

therefore,

the community studied by the realtors​ was not unusual