The following data represent the asking price of a simple random sample of homes

Question

The following data represent the asking price of a simple random sample of homes for sale. Construct a 99% confidence interval with and without the outlier included. Comment on the effect the outlier has on the confidence interval. (a) Construct a 99% confidence interval with the outlier included. (exist, exist) (b) Construct a 99% confidence interval with the outlier removed. (exist, exist) (c) Comment on the effect the outlier has on the confidence interval. The outlier caused the width of the confidence interval to decrease. The outlier caused the width of the confidence interval to increase. The outlier had no effect on the width of the confidence interval.

Explanation / Answer

for above (n-1=11) degree of freedom and 99% CI ; t=3.1058

therefore a) 99 % confidence interval =sample mean -/+ t*std error =171693 ; 319490

b)

after removing outlier 459900 from above data:

for above (n-1=10) degree of freedom and 99% CI ; t=3.1693

99 % confidence interval =sample mean -/+ t*std error = 178689 ; 273529

c)

the outlier caused the width of the confidence interval to increase.

X 237000 143000 459900 271500 279900 205800 270000 147800 219900 259900 187500 264900 mean(X) 245591.667 std deviation(S) 82423.424 std error =S/(n)1/2 23793.593

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