Question

In 2011 the U.S. Department of Transportation reported with 95% confidence that the average length of a motor vehicle trip in the United States was 9.72 miles with a margin or error of 0.22 miles.

With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between ________and_________ miles.

The level of confidence for this estimate is ________%.

Answer 1

Answer with explanation:

Given : The average length of a motor vehicle trip in the United States was 9.72 miles

The margin of error = 0.22 miles

Significance level : $\alpha=1-0.95=0.05$

The confidence interval for population mean is given by :-

$\overline{x}\pm E$

$9.72 \pm 0.22=(9.50,\ 9.94)$

Thus , with 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between 9.50 miles and 9.94 miles.

The level of confidence for this estimate is 95%.