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8.4 A city expressway using four lanes in each direction was studied to see whether drivers...

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

Lane1234
Observed count294276238192

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

Answer & Explanation Solved by verified expert
4.2 Ratings (747 Votes)

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
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