Question

A police officer is at a sobriety checkpoint, testing drivers to see if they are driving while intoxicated. A driver is assumed to be sober (Ho) unless there is evidence suggesting intoxication (Ha). When screening a driver, the police officer has two choices: to let the driver continue on his way (not reject the null hypothesis) or to arrest the driver for a DWI (reject the null hypothesis).

a.) If a police officer makes a Type I error, what happened? What might be a consequence of this mistake?

b.) If a police officer makes a Type II error, what happened? What might be a consequence of this mistake?

Please show step by step or explanation of how that became a conclusion.

Answer 1

Here our hypothesis is:

H0: The driver is sober vs

H1: The driver is intoxicated

A type I error is the false rejection of a true null hypothesis, ie concluding that we can reject the null hypothesis when it's infact true.

a) Here a Type I error would lead the police officer to conclude that the driver is intoxicated and subsequently arrest him when he is infact sober.

A Type II error, is the non-rejection of a false null hypothesis. This means that we fail to reject the null hypothesis, when it's actually false.

b) Here a Type II error would imply that the police officer after the test has concluded that the driver is sober and has let him go. The consequence of this is that since the driver is actually intoxicated, the police has let him go which might create problems further on the road.