Answer:
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
