Question

Toyota wants to know how its compact car compares in average gasoline mileage per gallon to Ford. 30 drivers are selected to drive the same route twice, once in each brand of car. Test whether Toyota’s mean is statistically lower at the 1% significance level.

Toyota	Ford
n 1= 30	n 2= 30
x ¯ 1= 26.8	x ¯ 2= 31.7
σ 1= 17.6	σ 2= 16.0

What are the appropriate null and alternative hypotheses?

Answer 1

null hypothesis: Ho:μ1-μ2			>=	0
Alternate hypothesis: Ha:μ1-μ2			<	0

for 0.01 level with left tail test , critical z=-2.33
Decision rule : reject Ho if test statistic z<-2.33

x1            =	26.80	x2            =	31.70
n1           =	30	n2           =	30
σ1           =	17.60	σ2           =	16.00
std error σx1-x2=√(σ21/n1+σ22/n2)    =			4.343
test stat z =(x1-x2-Δo)/σX1-x2     =(26.80-31.70)/4.343 =			-1.13

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that  Toyota’s mean is statistically lower at the 1% significance level.