Question

1. A highway with four lanes in each direction was studied to see whether drivers prefer certain lanes. A total of 1030 automobiles were observed during heavy early-morning traffic, and the number of cars in each lane was recorded: Lane 1 2 3 4 Observed count 294 276 238 222 Do the data present sufficient evidence to indicate that some lanes are preferred over others? Test using α = 0.01.

Answer 1

Hypotheses:

Ho: There is no preference ie all proportions are equal

Ha: there is the preference and at least one of them is not equal

We need to do the chi-square test

n=1030
Lane	Observed, O	Probability, p	Expected, E	(O-E)2/E
1	294	1/4	257.50	5.173786408
2	276	1/4	257.50	1.329126214
3	238	1/4	257.50	1.476699029
4	222	1/4	257.50	4.894174757
Total	1030	1	1030	12.87378641

Chi-sq test statistic = 12.874

degree of freedom = 4-1 = 3

p-value = 0.0049

Since the p-value is less than 0.01, we reject the null and conclude that some lanes are preferred over others