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Chapter 10: Q. 10.8 (page 581)

Two types of valves are being tested to determine if there is a difference in pressure tolerances. Fifteen out of a random sample of 100of Valve Acracked under 4500psi.Six out of a random sample of 100of Valve Bcracked under 4500psi.Test at a5% level of significance.

Short Answer

Expert verified

Sufficient evidence is obtained to conclude that the proportion of Valve A that cracked is not equal to the proportion of Valve B that cracked.

Step by step solution

01

Given information

Here,15out of a random sample of 100of Valve A cracked under 4500psiand 6out of a random sample of 100of Valve B cracked under 4500psi.Test at a 5%level of significance.

02

Calculation

The null and alternative hypothesis obtained are :

H0:pA=pBHa:pB鈮�pB

The significant level is, 伪=5%=0.05.

The p-value is localid="1650196586213" 0.0379,which is lower than the significant level.

Therefore, we reject the null hypothesis.

Hence, there is sufficient evidence to conclude that the proportion of Valve A that cracked is not equal to the proportion of Valve B that cracked.

03

Final answer

There is sufficient evidence to conclude that the proportion of Valve A that cracked is not equal to the proportion of Valve B that cracked.

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