You are the maker of batteries for heart pacemakers Your eng

You are the maker of batteries for heart pacemakers. Your engineers suggest that batteries last 300 days, i.e., H₀: battery life is 300 days and that H_A: battery life is <300 days. For the best of quality control for the success of your company and health of your clients, when testing the battery life:

Would you rather make a Type I or Type II error? {2}

Based on your answer (a), should use a high or low a-level and why? {2}

Solution

(a) When doing hypothesis testing, two types of mistakes may be made and we call them Type I error and Type II error.

Decision

Reality

H0 is true

H0 is false

Reject H0

Type I error

Correct

Fail to Reject H0

Correct

Type II error

If we reject H₀ when H₀ is true, we commit a Type I error. The probability of Type I error is denoted by:

If we fail to reject H₀ when H₀ is false, we commit a Type II error. The probability of Type II error is denoted by: .

H₀ = 300 , H_A = <300

We know that the battery life of pacemaker is 5-15 years, which indicates that H₀ is not true. Thua type I error is not committed over here.

Though the H₀ is false, company fail to reject H₀. Thus a type II is committed over here.

(b) Decrease the level of significance means decreased probability of type I error and increased probability of type II error.

So, based on the answer (a), the level of significance must be low.