Question

11) In the past, the mean battery life for a certain type of flashlight battery has been 8.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean battery life has increased as a result. The hypotheses are: Ho: = 8.8 hours H4> 8.8 hours a) Explain the result of a Type I error. b) Explain the result of a Type II error.

Answer 1

The null and alternative hypothesis is

H₀ : μ = 8.8 hours

H_a : μ > 8.8 hours

a. Type I error

Type I error is the error when we reject H₀ when H₀ is actually true.

In this case, we commit type I error if we reject H₀ when actually H₀ is true, that is when actually mean (μ) = 8.8 hours.

b. Type II error

Type II error is the error when we do not reject H₀ when H₀ is actually false.

In this case, we commit type II error if we do not reject H₀ when actually it is false, that is when actually mean ( μ) > 8.8 hours