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.

$161,000

$279,900

$219,900

$143,000

$205,800

$244,900

$459,900

$184,000

$187,500

$270,500

$147,800

$264,900

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.

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

Explanation / Answer

I have made use of scatter plot to figure out the outlier, and got that the outlier is 459900

First let us find the confidence interval with the outlier included

we get Mean (x bar) = 230758.3

Standard deviation (s) = 86399.77

Sample size n = 12

.

the formula for confidence interval is:

x bar - t*s/sqrt n , xbar + t*s/sqrt n

The value of t for df=11 and confidence 99% is 3.106

On plugging these values we get:

230758.3 - 3.106 * 86399.77 /sqrt 12 , 230758.3 + 3.106 * 86399.77 /sqrt 12

153290.1 , 292983.9

.

Now we find the confidence interval without the outlier

we got 11 numbers now , so df = 10 , for confidence level 99% we get t = 3.169

Mean (x bar) = 209927.3

s = 49834.69

209927.3 - 3.169 * 49834.69/sqrt(11) , 209927.3 + 3.169 * 49834.69/sqrt(11)

162310.8 , 257543.8

.

We can observe that when the outlier is removed, the confidence interval is more narrow. With the inclusion of the outlier we see that the mean and the standard deviation both get pulled towards the outlier, showing unwanted increase in their values, thus causing the confidence interval to widen

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