Suppose mu_1 and mu_2 are true mean stopping distances at 50 mph for cars of a c
ID: 3227188 • Letter: S
Question
Suppose mu_1 and mu_2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: s_1 = 5.09, n = 5, y = 129.8, and s_2 = 5.37. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system and cars equipped with system 1 and cars equipped with system 2. Does the interval suggest that precise information about the value of this difference is available? Because the interval is so narrow, it appears that precise information is available. Because the interval is so wide, it appears that precise information is not available. Because the interval is so narrow, it appears that precise information is not available. Because the interval is so wide, it appears that precise information is available.Explanation / Answer
(a)
n1 = 5
n2 = 5
x1-bar = 113.3
x2-bar = 129.8
s1 = 5.09
s2 = 5.37
% = 95
Degrees of freedom = n1 + n2 - 2 = 5 + 5 -2 = 8
Pooled s = (((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/DOF) = (((5 - 1) * 5.09^2 + ( 5 - 1) * 5.37^2)/(5 + 5 -2)) = 5.231873469
SE = Pooled s * ((1/n1) + (1/n2)) = 5.23187346941801 * ((1/5) + (1/5)) = 3.308927319
t- score = 2.306004133
Width of the confidence interval = t * SE = 2.30600413329912 * 3.30892731863364 = 7.630400074
Lower Limit of the confidence interval = (x1-bar - x2-bar) - width = -16.5 - 7.63040007355553 = -24.13040007
Upper Limit of the confidence interval = (x1-bar - x2-bar) + width = -16.5 + 7.63040007355553 = -8.869599926
The 95% confidence interval is [-24.13, -8.87]
(b) Option D.