Problem 11.3 Consider each of the hypothesis-testing applications below. Indicat

Question

Problem 11.3 Consider each of the hypothesis-testing applications below. Indicate for each outcome whether it is a correct decision, a type I error, or a type II error: (a) Ho :New power cell's lifetime does not exceed old one's (1) Change to new when old lasts as long or longer o Type I Error o Correct Decision o Type II Error (2) Keep old when new lasts longer Type 1 Error Type II Error o Correct Decision (3) Keep old when old lasts as long or longer Type II Error o Type I Error o Correct Decision (4) Change to new when new lasts longer Correct Decision Type I Error o Type II Error (b) Ho Memory chips are satisfactory (1) Reject satisfactory shipment Type II Error Type I Error o Correct Decision (2) Accept satisfactory shipment o Type II Error Correct Decision Type I Error (3) Reject unsatisfactory shipment. o Correct Decision Type I Error Type II Error (4) Accept unsatisfactory shipment. Type II Error o Type I Error Correct Decision

Explanation / Answer

Question 11.3:

Type I error is defined as the error of incorrectly rejecting the true null hypothesis while the type II error here is defined as the error of incorrectly retaining the false null hypothesis.

a) (i) Here we are given that even though the old one last as long as new, that is the null hypothesis is correct here, we are still changing the cell that is we reject the null hypothesis. Therefore there is type I error here.

(ii) Here we are given that new one lasts longer therefore null hypothesis is false but we are still using the old one and therefore not rejecting the null hypothesis. Therefore there is type II error here.

(iii) Here the null hypothesis is true and it is not rejected. Therefore Correct decision

(iv) Here the null hypothesis is false and it is rejected. Therefore Correct decision

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