In 2011 the U.S. Department of Transportation reported with 95% confidence that

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 5.895 and 13.545 # miles. The level of confidence for this estimate is 95 Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity

Explanation / Answer

Ans:

1)Given that

95% confidence interval for average length

=9.72+/-0.22

Lower limit=9.72-0.22=9.50

Upper limit=9.72+0.22=9.94

2)

df=24-1=23

critical t value=tinv(0.02,23)=2.500

98% confidence interval for true mean

=30+/-2.50*(7/sqrt(24))

=30+/-3.6

=(26.4, 33.6)

lower limit=26.4

upper limit=33.6

When confidence level is increased,which means that we want to be more sure that population mean falls between CI limits,which will need wider confidence interval hence larger margin of error.

Larger the confidence level,larger the z multiplier value,so larger margin of error.

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