Question

Traffic speed: The mean speed for a sample of

36

cars at a certain intersection was

25.84

kilometers per hour with a standard deviation of

2.34

kilometers per hour, and the mean speed for a sample of

138

motorcycles was

38.85

kilometers per hour with a standard deviation of

3.84

kilometers per hour. Construct a

99

%

confidence interval for the difference between the mean speeds of motorcycles and cars at this intersection. Let

μ1

denote the mean speed of motorcycles and round the answers to at least two decimal places.

A 99 % confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is <<−μ1μ2 .

Answer 1

	Motorcycles	Cars
sample mean x =	38.850	25.840
std deviation s=	3.840	2.340
sample size n=	138	36
Point estimate =x1-x2=		13.010
std error =√(S21/n1+S22/n2)=		0.5089

Point estimate of differnce =x1-x2     =		13.010
for 99 % CI & 35 df value of t=		2.724	from excel: t.inv(0.995,35)
margin of error E=t*std error                   =		1.386
lower bound=mean difference-E     =		11.6238
Upper bound=mean differnce +E      =		14.3962
from above 99% confidence interval for population mean =(11.62 <µ1-µ2<14.40 )