3. A traffic engineer feels that on a certain four-lane highway, the probability of being in the innermost lane (Lane 1) is twice as great as any of the other lanes. You can assume the other lanes (2, 3, and 4) have equal probabilities. A random sample of 200 motorists is chosen and the lanes in which they are travelling is noted. The results are given in the following table.

TRAFFIC LANES

Lane 1 2 3 4

Frequency55456238

a. At the 0.05 significance level, does the traffic data support the assumption of the traffic engineer? (16 pts)

3. (continued) In addition to the lane a particular car is traveling in, for the same 200 cars, data is collected on the part of the world where the car headquarters are located. Cars are classified as U.S., Europe, and Pacific Rim. The table below has that information.

TRAFFIC LANES

1 23 4

Europe10102516

Pacific Rim17182112

US28171610

b. What type of test would you conduct to see if there is a relationship between the car headquarters and the lane the car is travelling in? (3 pts)

c. If alpha = 0.01, what would the CRITICAL value be for the test you suggest in part (b)? (4 pts)

d. What are the expected frequencies for the following cells: (2 pts each)

Europe and lane 3____________________

Pacific Rim and lane 1____________________

US and lane 4____________________