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Chapter 10: Q. T10.12 (page 699)

A random sample of 100of last year鈥檚 model of a certain popular car found that 20had a specific minor defect in the brakes. The automaker adjusted the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350of this year鈥檚 model found that 50had the minor brake defect.

a. Was the company鈥檚 adjustment successful? Carry out an appropriate test to support your answer. b. Based on your conclusion in part (a), which mistake鈥攁 Type I error or a Type II error鈥攃ould have been made? Describe a possible consequence of this error.

Short Answer

Expert verified

a. The answer isP=P(Z>1.39)=P(Z<-1.39)=0.0823

b. Failure to reject the null hypothesis is a type II mistake.

Step by step solution

01

Part (a) Step 1: Given information

We have to tell about was the company鈥檚 adjustment successful

02

Part (a) Step 2: Explanation

It has been given that

x1=20,x2=50,n1=100,n2=350

p^2=x2n2=50350鈮�0.1429

z=p^1-p^2p^p1-p^p1n1+1n2=0.2-0.14290.1556(1-0.1556)1100+1350鈮�1.39

The values using the table

P=P(Z>1.39)=P(Z<-1.39)=0.0823

03

Part (b) Step 1: Given information

We have to tell possible consequence of this error.

04

Part (b) Step 2: Explanation

The null hypothesis H was not rejected.

  • Type I blunder: H should be rejected as a null hypothesis, if H 0H is true as the null hypothesis.

Failure to reject the null hypothesis is a type II mistake.

If the null hypothesis H is false, then

It's only feasible that we made.

  • Type II error because we didn't reject the null hypothesis H .

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