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. Click the icon to view the table of areas under the t-distribution. Construct a 99% confidence interval with the outlier included. (Round to the nearest integer as needed.) Construct a 99% confidence interval with the outlier removed. (Round to the nearest integer as needed.) Comment on the effect the outlier has on the confidence interval. The outlier caused the width of the confidence interval to increase. The outlier had no effect on the width of the confidence interval. The outlier caused the width of the confidence interval to decrease.

Explanation / Answer

(a) Outlier included:

mean = m = 219683.33

standard deviation = s = 86268.46

z99.5 = 2.575829

Confidence interval: m - z99.5*s ,  m + z99.5*s

= (219683.33 - 2.575829*86268.46 , 219683.33 + 2.575829*86268.46)

= ( -2529.47 , 441896.13 )

(b) Outlier removed:

mean = m = 197927.27

standard deviation = s = 44029.15

z99.5 = 2.575829

Confidence interval : m - z99.5*s ,  m + z99.5*s

= (197927.27 - 2.575829*44029.15 , 197927.27+ 2.575829*44029.15)

= ( 84515.71 , 311338.83 )

(c) The outlier caused the width of the confidence interval to increase.

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