A police officer uses a motion detector to indicate whether a car is traveling faster than the speed limit (speeding). A speeding ticket will be issued to the driver of the car if the officer believes the driver is speeding, as indicated by the detector. The situation is similar to using a null and an alternative hypothesis to decide whether to issue a ticket. The hypotheses can be stated as follows.

H0 : The driver is not speeding.

Ha : The driver is speeding.

Which of the following best describes the power of the test?

(A) The probability of issuing a ticket to a driver who is speeding

(B) The probability of issuing a ticket to a driver who is not speeding

(C) The probability of not issuing a ticket to a driver who is speeding

(D) The probability of not issuing a ticket to a driver who is not speeding

(E) The probability that the motion detector is working correctly

Question

Ami

Mathematics

26 January, 10:47

A police officer uses a motion detector to indicate whether a car is traveling faster than the speed limit (speeding). A speeding ticket will be issued to the driver of the car if the officer believes the driver is speeding, as indicated by the detector. The situation is similar to using a null and an alternative hypothesis to decide whether to issue a ticket. The hypotheses can be stated as follows.

H0 : The driver is not speeding.

Ha : The driver is speeding.

Which of the following best describes the power of the test?

(A) The probability of issuing a ticket to a driver who is speeding

(B) The probability of issuing a ticket to a driver who is not speeding

(C) The probability of not issuing a ticket to a driver who is speeding

(D) The probability of not issuing a ticket to a driver who is not speeding

(E) The probability that the motion detector is working correctly

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Answers (1)

Know the Answer?

Jaylee · Answer 1

A. The probability of issuing a ticket to a driver who is speeding

Step-by-step explanation:

The power of the test is the probability of rejection of null hypothesis when it is false. Power of the test is the complement of type of II error so, it is denoted by 1-β.

The given null hypothesis is driver is not speeding and alternative hypothesis is driver is speeding. If the null hypothesis is rejected then we can say that driver is speeding. Also, when the null hypothesis is rejected when it is false then the speeding driver will get a ticket. So, the power of the test is "The probability of issuing a ticket to a driver who is speeding".