(c)For the mileage values in this sample, 36.4 thousand miles is more extreme than 25.3 thousand miles is, that is, 36.4 is farther from the sample mean mileage than 25.3 is. How would the 90% confidence interval for the mean used selling price when the mileage is 36.4 thousand miles compare to the 90% confidence interval for the mean used selling price when the mileage is 25.3 thousand miles? The intervals would be identical. The interval computed from a mileage of 36.4 thousand miles would be narrower and have a different center. The interval computed from a mileage of 36.4 thousand miles would be wider but have the same center. The interval computed from a mileage of 36.4 thousand miles would be narrower but have the same center. The interval computed from a mileage of 36.4 thousand miles would be wider and have a different center.
Question
(c)For the mileage values in this sample, 36.4 thousand miles is more extreme than 25.3 thousand miles is, that is, 36.4 is farther from the sample mean mileage than 25.3 is. How would the 90% confidence interval for the mean used selling price when the mileage is 36.4 thousand miles compare to the 90% confidence interval for the mean used selling price when the mileage is 25.3 thousand miles?
The intervals would be identical.
The interval computed from a mileage of 36.4 thousand miles would be narrower and have a different center.
The interval computed from a mileage of 36.4 thousand miles would be wider but have the same center.
The interval computed from a mileage of 36.4 thousand miles would be narrower but have the same center.
The interval computed from a mileage of 36.4 thousand miles would be wider and have a different center.
Solution
The interval computed from a mileage of 36.4 thousand miles would be wider and have a different center.
This is because the confidence interval is a range of values, derived from the statistical analysis of the sample data, within which the true value for the population is likely to fall. Since 36.4 thousand miles is more extreme (farther from the mean) than 25.3 thousand miles, the variability or uncertainty is greater, leading to a wider confidence interval. Additionally, the center of the interval would shift because the mean used selling price would likely be different for cars with 36.4 thousand miles versus those with 25.3 thousand miles.
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