Question

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 8484 cars owned by students had an average age of 5.78 years. A sample of 118 cars owned by faculty had an average age of 5.79 years. Assume that the population standard deviation for cars owned by students is 2.39 years, while the population standard deviation for cars owned by faculty is 3.27 years. Determine the 98%confidence interval for the difference between the true mean ages for cars owned by students and faculty.

Step 1 of 3 :  

Find the point estimate for the true difference between the population means.

Answer 1

Since , the population standard deviatios are known.

Therefore , use normal distribution.

Part 1 of 3 :

The point estimate for the true difference between the population means is ,

Part 2 of 3 :

Now , ; From standard normal distribution table

Therefore , the margin of error is ,

Part 3 of 5 :

The 98%confidence interval for the difference between the true mean ages for cars owned by students and faculty is ,