Question

8.4 A city expressway using four lanes in each direction was studied to see whether drivers preferred to drive on the inside lanes. A total of 1,000 automobiles was observed during the heavy heavy morning traffic and their respective lanes were recorded. The results were as follow:

Lane	1	2	3	4
Observed count	294	276	238	192

Do the data present sufficient evidence to indicate that some lanes are preferred over others? Use a = 0.05.

Answer 1

Null hypothesis: Ho:All lanes are equally preferred

Alternate hypothesis:Ha: some lanes are preferred over others

degree of freedom =categories-1=			3
for 0.05 level and 3 df :crtiical value X2 =				7.815
Decision rule: reject Ho if value of test statistic X2>7.815

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
1	0.2500	294.0	250.00		7.7440
2	0.2500	276.0	250.00		2.7040
3	0.2500	238.0	250.00		0.5760
4	0.2500	192.0	250.00		13.4560
total	1.000	1000	1000		24.4800
test statistic X2 =		24.480

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that some lanes are preferred over others