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.

164500,143000,459900,200500,279900,205800,181900,147800,219900,242900,187500,264900,

a. Construct a 99% confidence interval with the outlier included.

($___, $___)

b.Construct a 99% confidence interval with the outlier removed.

c.Comment on the effect the outlier has on the confidence interval.

Explanation / Answer

a) Sample mean would be = $224875

Sample Standard deviation = $85656.34

Margin of error = (T.INV(0.99+(0.01/2),11)*85656.34)/Sqrt(12) = 76796.83

99% Interval

($224875-$76796.83, $224875+$76796.83)

= ($148078, $301672)

So, Interval is ($148078, $301672)

b) We will remove $459900 from the data

Sample mean would be = $203509.1

Sample Standard deviation = $45220.38

Margin of error = (T.INV(0.99+(0.01/2),10)*45220.38)/Sqrt(11) = 43211.32

99% Interval

($203509.1-$43211.32, $203509.1+$43211.32)

= ($160298, $246720)

So, Interval is ($160298, $246720)

c) Outlier will increase the Width of interval

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