Why is there always a chance of making a mistake (an incorrect decision) in any hypothesis test?
Because we usually control the value of a, one could simply set the probability of a type I error to a very small value, say 0.0001. What’s wrong with this strategy?
The 30-mile I-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 140,000 vehicles cross this bridge every day.10 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.
a. Write the null and alternative hypotheses about
mean number of cars per day that cross the Tappan Zee Bridge.
b. For the hypotheses in part (a), describe the type I and type II errors.
c. If a type I error is committed, who is more angry, the transportation officials or drivers, and why? d. If a type II error is committed, who is more angry, the transportation officials or drivers, and why?