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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≠pB

The significant level is, α=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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Most popular questions from this chapter

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

Calculate the test statistic.

Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller.

Draw the graph of the p-value.

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