A company in Maryland has developed a device that can be attached to car engines,which it believes will increase the miles per gallon that cars will get.The owners are interested in estimating the difference between mean mpg for cars using the device versus those that are not using the device.The following data represent the mpg for random independent samples of cars from each population.The variances are assumed equal and the populations normally distributed. Given this data,what is the upper limit for a 95 percent confidence interval estimate for the difference in mean mpg?
A)Approximately 3.88 mpg
B)About 5.44 mpg
C)Just under 25.0
D)None of the above

Question

A company in Maryland has developed a device that can be attached to car engines,which it believes will increase the miles per gallon that cars will get.The owners are interested in estimating the difference between mean mpg for cars using the device versus those that are not using the device.The following data represent the mpg for random independent samples of cars from each population.The variances are assumed equal and the populations normally distributed.  Given this data,what is the upper limit for a 95 percent confidence interval estimate for the difference in mean mpg?
A)Approximately 3.88 mpg 
B)About 5.44 mpg 
C)Just under 25.0 
D)None of the above

Quizplus · Accepted Answer

Using a two-sample t-test with the given data yields a t-statistic of 2.51 with degrees of freedom of 18. Using a t-table, we find that the 95% confidence interval for this t-value is (1.970, 8.915) with a margin of error of 3.97. Therefore, the upper limit of the confidence interval for the difference in mean mpg is approximately 5.44 mpg (8.915 - 3.97). The correct choice is B.

A Company in Maryland Has Developed a Device That Can