Question

4. The main access road to suburban shopping mall sometimes becomes severely congested. On weekdays, excluding holidays, the average number of vehicles going toward the mall between 9:00 AM and 7:00 PM that pass a counter is 11,260. The highway department tried to improve traffic flow by changing stoplight cycles and improving turn lanes. For the first seven non-holiday weekdays after the changes, the volumes were 10,690, 11,452, 12,316, 12, 297, 11,889, 10911, and 12,647. A local politician who reviewed the results said that the data proved there had been significant improvement in traffic volume. At 5% level of significance, is this a reasonable conclusion to draw from the given data? Please show the necessary steps and explain your conclusion. What will happen to the probability of type II error if you were to redo the test at 1% level of significance?

Answer 1

Solution

Given data

10,690, 11,452, 12,316, 12, 297, 11,889, 10911, and 12,647

Number of samples = 7

Mean = (10690 + 11452 + 12316 + 12297 + 11889 + 10911 + 12647)/7
= 82202/7
  = 11743.14

Standard deviation = 748.2748

probability of type II error if you were to redo the test at 1% level of significance