Question

A car manufacturer advertises that its new ‘ultra-green’ car obtains on average 100 miles per gallon (mpg). A consumer advocacy group tested a sample of 25 cars. Each car was driven the same distance in similar conditions, and the following results on mpg were recorded:

112	111	85	88	99
96	83	87	101	102
113	93	102	92	96
79	117	113	90	78
98	89	99	102	96

Using Descriptive Statistics of Data Analysis of Excel with a 90% confidence level, the following incomplete output is available:

Mean	96.84
Standard Deviation	10.79228119
Sample Variance	116.4733333
Count	25
Confidence Level(90.0%)	3.692864099

a. The margin of error of the 90% confidence interval for the mean mpg of all new ‘ultra-green’ cars is

(Remember that Excel actually shows the margin of error of the confidence interval for the assumed confidence level of 90%)

   b. The 90% confidence interval for the mean mpg of all new ‘ultra-green’ cars is

c. What is the sample proportion of the ‘ultra-green’ cars that obtain over 100 mpg?

d. What is the margin of error of the 90% confidence interval for the proportion of all new ‘ultra-green’ cars that obtain over 100 mpg?

Answer 1

SolutionA:

margin of error can be found using excel as

=CONFIDENCE.T(0.1;10.79228119;25)

=3.692864

SolutionB:90% confidence interval for mean is

mean-MOE,mean+MOE

=96.84-3.692864,and 96.84+3.692864

=93.14714,100.5329

The 90% confidence interval for the mean mpg of all new ‘ultra-green’ cars lies in between

93.14714 and 100.5329

Solutionc:

sample proportion=9/25=0.36

Solutiond:

the margin of error of the 90% confidence interval for the proportion of all new ‘ultra-green’ cars that obtain over 100 mpg?

MOE=Z*sqrt(p^(-p^)/n

=1.645*sqrt(0.36*(1-0.36)/25)

=0.15792

ANSWER:0.15792