$280,500 $279,900 $219,900 $205,800 $172,500 $195,000 $147,800 $264,900 17. The
ID: 3321474 • Letter: #
Question
$280,500 $279,900 $219,900 $205,800 $172,500 $195,000 $147,800 $264,900 17. 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. 1 Click the icon to view the table of areas under the t-distribution. $143,000 $459,900 $265,900 $187,500 (a) Construct a 99% confidence interval with the outlier included. Round to the nearest integer as needed.) (b) Construct a 99% confidence interval with the outlier removed. Round to the nearest integer as needed.) (c) Comment on the effect the outlier has on the confidence interval O O O The outlier caused the width of the confidence interval to increase. The outlier caused the width of the confidence interval to decrease. The outlier had no effect on the width of the confidence interval.Explanation / Answer
The formula for estimation is:
= M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = (s2/n)
Calculation
M = 235216.6
t = 2.58
sM = (86036.732/12) = 24836.66
= M ± Z(sM)
= 235216.6 ± 2.58*24836.66
= 235216.6 ± 63975.009
Result
M = 235216.6, 99% CI [171241.591, 299191.609].
You can be 99% confident that the population mean () falls between 171242 and 299192.
Here the outliers is - 459900
No calculating 99% CI with outlier removed
Calculation
M = 214790.9
t = 2.58
sM = (51335.742/11) = 15478.31
= M ± Z(sM)
= 214790.9 ± 2.58*15478.31
= 214790.9 ± 39869.479
Result
M = 214790.9, 99% CI [174921.421, 254660.379].
You can be 99% confident that the population mean () falls between 174921 and 254660.
The outlier caused the width of the confidence interval to increase.
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