[8 points] The 30-mile 1-287 corridor near Tarrytown, New York, is heavily trave
ID: 3309903 • Letter: #
Question
[8 points] The 30-mile 1-287 corridor near Tarrytown, New York, is heavily traveled and is a major interstate transportation link. The Tappan Zee Bridge is part of this road network and is in need of structural repairs. Approximately 140000 vchicles cross this bridge every day Transportation officials have decided to conduct a hypothesis test and will raise tolls to fund planned repairs if there is evidence to suggest that the mean number of cars per day using this bridge has increased. [2 points each] 3. (a) write the null and alternative hypotheses about , the mean number of cars per day that (b) For the hypotheses in part (a), describe the Type I and Type II errors in the context of the (c) If a Type I error is committed who is more angry, the transportation officials or drivers, (d) If a Type lIl error is committed who is more angry, the transportation officials or drivers, cross the Tappan Zee Bridge, that the transportation officials would want to test. problem. and why? and why?Explanation / Answer
(a) The hypothesis is:
Null hypothesis H0 : The mean number of cars using the bridge has not significantly increased from 140000.
Alternate hypothesis H1: The mean number of cars using the bridge has significantly increased from 140000.
(b)
Type 1 error is : Reject H0, i.e., reject the hypothesis that the mean number of cars has not increased, when in reality we should be not be rejecting it. That is, concluding that the mean number of cars has increased, when in reality it has NOT.
Type 2 error is : Failing to reject the null hypothesis H0, when in reality we should reject it. That is, concluding that the mean number of cars has NOT increased, when in reality it has.
(c) If there is type 1 error, then it means that in reality the mean number of cars has not increased, however it is concluded that it has increased. Thus the repair work would be done based on the conclusion, when it is not really required. Hence, the transportation officials would be angry.
(d) If there is type 2 error, then it means that in reality the mean number of cars has increased significantly, however it is concluded that it has not. Thus the repair work would NOT be done based on the conclusion, when it is required. Hence, the drivers would be angry.
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