1. A real estate agent has collected a random sample of 75 houses that were rece

Question

1.       A real estate agent has collected a random sample of 75 houses that were recently sold in a suburban community. She is particularly interested in comparing the appraised value and recent selling price of the houses in this particular market. The data are provided in the file Houses.xlsx. Let µA-P be the mean difference between appraised value and price, respectively.

a)       Using this sample data, calculate a 95% confidence interval for µA-P. Is there any evidence that values of houses tend to be over- or under-estimated? Discuss.

b)      Test, at = 10% significance level, the following hypotheses: H0: µA-P 0 vs. H0: µA-P > 0. Is there evidence that values of the houses tend to be over-estimated? Discuss

   Link for House.xls -    https://drive.google.com/file/d/0BwnfLKPdeFBbZWhhNXNKRmdmZDA/view?usp=sharing

Explanation / Answer

(a) Here Mean xA-P = - $ 452

Standard deviation of deviation sA-P = $ 11021

Here dF = 74 and alpha = 0.05 (95% confidence interval)

t74,0.05 = 1.9925

standard error of the difference se0 = sd /sqrt(n) = 11021/ sqrt(75) = $ 1272.60

95% confidence level =  xA-P +- t74,0.05 * se0  

= - 452 +- 1.9925 * 1272.60

= (-2987.66, 2083.66)

(b) at = 10% significance level, the following hypotheses: H0: µA-P 0 vs. Ha: µA-P> 0.

Here t - test

t = (xA-P )/ se0 = - 452/ 1272.60 = - 0.3552

Here critical value of t for one tailed hypothesis test.

tcr = t0.1,74 = 1.2931

so here l t l < tcr so we shallnot reject the null hypothesis and can conclude that values of the housesare not to be over-estimated

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