Question

A recent study looked at the price of new compact sedans around the country.

From the data, they constructed a 95% confidence interval to estimate the true mean price of new compact sedans around the country. The resulting interval is given:
($10,430, $12,030)
What must have been the value of the sample mean price of compact sedans from the data that was collected?

A• $12,030
B• There is not enough information to answer this question.
C• $11,230
D• $10,430
E• $22,460

Answer 1

The sample mean price of compact sedans from the data that was collected must be $11,230 since it is directly in the middle of the 95% confidence interval provided, which is ($10,430, $12,030). Therefore correct option is C

Step-by-step explanation:

The confidence interval provided is ($10,430, $12,030). A confidence interval is constructed based around the sample mean, with the margin of error added and subtracted to find the lower and upper bounds respectively. Because the confidence interval is symmetric about the mean, the mean is directly in the middle of the interval.

To find the sample mean, we take the average of the lower and upper bounds of the confidence interval:

Sample Mean = (Lower Bound + Upper Bound) / 2

Sample Mean = ($10,430 + $12,030) / 2

Sample Mean = $22,460 / 2

Sample Mean = $11,230

Therefore, the answer is C) $11,230.