Question

13. [6 points] Suppose that when one of our beloved local food delivery robots approaches an intersection, it performs a hypothesis test with the hypotheses Ho: It is not safe to cross the street H: It is safe to cross the street a) Briefly describe the consequences of a Type 1 Error in this situation. b) Briefly describe the consequences of a Type II Error in this situation. c) Based on your previous answers, which of the below is the most reasonable? A. a should be set fairly high (like 0.20), as a Type I Error is worse B. a should be set fairly low (like 0.01), as a Type 1 Error is worse C. a should be set fairly high (like 0.20), as a Type II Error is worse D. a should be set fairly low (like 0.01), as a Type II Error is worse

Answer 1

(a)

Type I Error: Rejection of a true null hypothesis.

Suppose in reality it is not safe to cross the street. But the robot wrongly concludes that it is safe to cross the street. So, the robot crosses the street when the street is busy and hence it meets with accident.

(b)

Type II Error: Failure to reject a false null hypothesis.

Suppose in reality it is safe to cross the street. But the robot wrongly concludes that it is not safe to cross the street. So, the robot does not cross even when the street is free and hence there is delay is food supply unnecessarily.

(c)

Correct option:

B.   $\alpha$ should be set fairly low (like 0.01) as Type I error is worse.

Explanation:

The probability of Type I error is minimized by setting a fairly low (like 0.01) for $\alpha$ , because by committing Type I Error, the robot crosses the street when the street is busy and hence it meets with accident.