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 263 cars owned by students had an average age of 7.25 years. A sample of 291 cars owned by faculty had an average age of 7.12 years. Assume that the population standard deviation for cars owned by students is 3.77 years, while the population standard deviation for cars owned by faculty is 2.99 years. Determine the 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty

Step 2 of 3 :  

Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places. point of estimate= .13

Answer 1

= 7.25 ,   = 7.12

n1 = 263 , n2 = 291

= 3.77 , =  2.99

C= 90%

1)

formula for confidence interval is

Where Zc = 1.645

−0.3489 <    < 0.60889

Thus we get 90% confidence interval as ( −0.3489 , 0.6089)

2)

formula for margin of error is

Margin of error = 0.478928