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 independent random samples of cars from each population.The variances are assumed equal and the populations normally distributed. Given this data,what is the critical value if the owners wish to have a 90 percent confidence interval estimate?
A)t = 2.015
B)t = 1.7823
C)z = 1.645
D)z = 1.96

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 independent random samples of cars from each population.The variances are assumed equal and the populations normally distributed.  Given this data,what is the critical value if the owners wish to have a 90 percent confidence interval estimate?
A)t = 2.015 
B)t = 1.7823 
C)z = 1.645 
D)z = 1.96

Quizplus · Accepted Answer

Since the sample sizes are small (both less than 30) and the population variances are assumed to be equal, we use a pooled t-test. With a 90% confidence interval, the degrees of freedom are n1+n2-2=18. Using a t-table, we find the critical value to be 1.7823. Therefore, the correct choice is B.

A Company in Maryland Has Developed a Device That Can