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%. a. describe the consequences of type i and type ii errors. b. should the engineer design the test with a higher alpha or a higher beta? explain.

Answer 1

Type I error occurs when the engineer incorrectly rejects the null hypothesis and concludes that the engines are unsafe when they are actually safe. Type II error occurs when the engineer incorrectly fails to reject the null hypothesis and concludes that the engines are safe when they are actually unsafe. The engineer should design the test with a higher alpha to minimize the chances of a Type II error.

Step-by-step explanation:

a. Type I error occurs when the engineer incorrectly rejects the null hypothesis and concludes that the engines are unsafe when they are actually safe. This could result in unnecessary grounding of safe airplanes and unnecessary expenses. Type II error occurs when the engineer incorrectly fails to reject the null hypothesis and concludes that the engines are safe when they are actually unsafe. This could lead to the operation of faulty engines, endangering lives. Both errors have significant consequences.

b. The engineer should design the test with a higher alpha. The alpha level, or significance level, is the probability of making a Type I error. In this case, a higher alpha level would result in a lower threshold for rejecting the null hypothesis, meaning the engineer would be more likely to detect unsafe engines and minimize the chances of a Type II error.