Question

An engineer is designing an experiment to test if airplane engines are faulty and unsafe to fly. the engineer expects 0.0001% of engines to be unsafe. the null hypothesis is that the probability of an unsafe engine is less than or equal to 0.0001% and the alternative hypothesis is that the probability the engine is unsafe is greater than 0.0001%.

describe the consequences of type i and type ii errors.

Answer 1

A Type I error in the context of airplane engine safety would lead to the unnecessary grounding of aircrafts and economic losses, while a Type II error could result in using unsafe engines, endangering passenger safety.

Step-by-step explanation:

In the context of hypothesis testing in statistics, an engineer is designing an experiment to test if airplane engines are faulty. The null hypothesis states that the probability of an unsafe engine is less than or equal to 0.0001%, while the alternative hypothesis suggests that the probability is greater than 0.0001%. It is crucial to understand the potential errors that can occur in this scenario: the Type I error and the Type II error.

A Type I error refers to the mistake of rejecting the null hypothesis when it is in fact true. In the case of the airplane engines, a Type I error would occur if the engineer concludes that airplane engines are unsafe when they are actually safe. The consequence of this error is significant, as it could lead to unnecessary grounding of aircrafts, economic losses, and unwarranted fear among the public.

Conversely, a Type II error happens when a false null hypothesis is not rejected. In the context of the airplane engines, a Type II error would occur if the engineer deems the engines safe when they are actually unsafe. This error is particularly dangerous as it could lead to the use of defective engines, posing a serious risk to passenger safety and potentially resulting in catastrophic accidents.