the following data represents the asking price of a simple r

the following data represents the asking price of a simple random  sample of homes for sale.  construct a 99% confidence level with and without the outlier included. comment on the effect the outlier has on the confidence interval.  

290,500, 279,900, 219,900

143,000, 205,800, 279,900

459,900, 181,900, 187,500

267,500,147,800, 264900

a.  Construct a 99% confidence interval with outlier included  _____,_______

Round to nearest integer

b.  construct a 99% confidence interval with outlier removed _____,______

Round to nearest integer

Comment on the effect that the outlier has on the confidence interval

1. the outlier causes the width of the confidence interval to decrease

2.  the outlier causes the width of the confidence interval to increase

3.   outlier has no effect on width of confidence interval

Solution

(a) sample mean=244041.7

sample standard deviatoin=85751.16

sample size =12

The degree of freedom =n-1=12-1=11

Given a=1-0.99=0.01, t(0.005, df=11)=3.11 (from student t table)

So the lower bound is

xbar - t*s/vn =244041.7-3.11*85751.16/sqrt(12) =167056

So the upper bound is

xbar + t*s/vn=244041.7+3.11*85751.16/sqrt(12)=321027

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(b) 459900 is removed

sample size=11

sample mean=224418.2

sample standard deviation=54822.58

The degree of freedom =n-1=11-1=10

Given a=0.01, t(0.005, df=10) =3.17 (from standard normal table)

So the lower bound is

xbar - t*s/vn =224418.2-3.17*54822.58/sqrt(11) =172019

So the upper bound is

xbar + t*s/vn=224418.2+3.17*54822.58/sqrt(11)=276817

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2.  the outlier causes the width of the confidence interval to increase