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.

Here is the information:

$232,000          $279,000          $219,900

$143,000          $205,800          $182,900

$459,900          $178,500          $187,500

$273,000          $147,800          $264,900

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:

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

ii) The outlier caused the width of the confidence interval to decrease.

iii) The outlier had no effect on the width of the confidence interval

Explanation / Answer

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.

Here is the information:

$232,000          $279,000          $219,900

$143,000          $205,800          $182,900

$459,900          $178,500          $187,500

$273,000          $147,800          $264,900

A) Construct a 99% confidence interval with the outlier included: ($144723.85 , $ 307642.82)

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

85280.08222

Sample Mean

$231,183

Sample Size

12

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

24618.23921

Degrees of Freedom

11

t Value

3.1058

Interval Half Width

76459.4878

Confidence Interval

Interval Lower Limit

154723.85

Interval Upper Limit

307642.82

B) Construct a 99% confidence interval with the outlier removed: ($164630.37 , $ 256151.45)

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

47888.1291

Sample Mean

$210,391

Sample Size

11

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

14438.8142

Degrees of Freedom

10

t Value

3.1693

Interval Half Width

45760.5393

Confidence Interval

Interval Lower Limit

164630.37

Interval Upper Limit

256151.45

C) Comment on the effect the outlier has on the confidence interval:

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

ii) The outlier caused the width of the confidence interval to decrease.

iii) The outlier had no effect on the width of the confidence interval

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

85280.08222

Sample Mean

$231,183

Sample Size

12

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

24618.23921

Degrees of Freedom

11

t Value

3.1058

Interval Half Width

76459.4878

Confidence Interval

Interval Lower Limit

154723.85

Interval Upper Limit

307642.82

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