Question

When not more than two valves of different sizes are mounted singly. the relieving capacity of the smaller valve shall not be less than _______ percent of the larger valve.

a) 20%
b) 35%
c) 50%
d) 70%

Answer 1

To determine if there is a significant difference in the pressure tolerances of two types of valves, a two-proportion z-test is performed at a 5 percent level of significance using the provided sample data to compare the proportions of each valve type that cracked under a certain pressure.

Step-by-step explanation:

The question relates to hypothesis testing, where we are trying to determine if there is a significant difference between two proportions - the proportion of Valve A and Valve B that cracked under a certain pressure. To test this, we can use a two-proportion z-test at the 5 percent level of significance.

The null hypothesis (H0) is that there is no difference in the proportion of valves that crack under 4,500 psi, while the alternative hypothesis (H1) is that there is a difference. Using the sample data provided, we calculate the test statistic and compare it to the critical value or p-value associated with a 5% level of significance.

If the calculated test statistic exceeds the critical value or if the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference between the two valve types. If the test statistic is less than the critical value and the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is not a significant difference between the two valves.