A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 64 cars owned by students had an average age of 6.27 years. A sample of 40 cars owned by faculty had an average age of 7.64 years. Assume that the population standard deviation for cars owned by students is 2.64 years, while the population standard deviation for cars owned by faculty is 3.42 years. Determine the 80% 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.

Margin of error = 0.81

Upper limit = -0.56

Lower limit =  -2.18

Step-by-step explanation:

Given Data;

                     Sample size      Sample mean      population deviation S.D

Sample 1            n₁= 64            x1-bar = 6.27                   б₁ = 2.64

Sample 2;           n₂ = 40         x2 -bar  = 7.64                б₂ = 3.42

For 80% interval, a = 1-0.8 = 0.2

From normal standard table,

the critical value of (a/2 = 0.2/2) =0.1 is 1.28

That is, Z = 1.28

Calculating the margin of error, we have

Margin of error = Z * √(б²₁/n₁ + б²₂/n₂)

                         = 1.28 * √(2.64²/64 + 3.42²/40)

                         = 1.28  * √0.1089 +  0.29241

                         = 1.28  * √0.40131

                         =0.81

Lower and upper limit of 80% interval for the difference between the true mean ages for cars owned by student and faculty is calculated as

Lower limit = (x1 - x2) - margin of error

                  = (6.27-7.64) - 0.81

                  = -2.18

Upper limit = (x1 - x2) + margin of error

                  = (6.27-7.64) + 0.81

                  = -0.56

step-by-step explanation:

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.