A building contractor has built a large number of houses of a about the same siz

Question

A building contractor has built a large number of houses of a about the same size and value. The contractor claims that the average value of these houses does not exceed $95,000. A real estate appraiser randomly selected five of the new homes built by the contractor and assessed their values as $94,000, $97,000, $96,000, $95,000, and $95,500. Test at the .05 level of significance. Do the five appraisals contradict the building contractor’s claim? Explain. (Set up the Null & Alternative Hypotheses and test using a critical value(s) & test statistic.)

Explanation / Answer

here null hypothesis: mean >=95000

alternate hypothesis:mean <95000

here for 0.05 level, crtiical value of t for 4 df =2.1318

hence test stat t=(X-mean)/std error =(95500-95000)1118.034 =0.4472

for which p value =0.338

as p value is greater then 0.05, we can not reject null hypothesis, and discard contractor claim

X 94000.000 97000.000 96000.000 95000.000 95500.000 mean(X) 95500.000 std deviation(S) 1118.034 std error =S/(n)1/2 353.553

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