Answer :
Final answer:
To test valve functionality, a chi-square test for independence can compare pressure tolerances of two valves at a 5 percent level of significance. If the p-value is less than 0.05, it suggests a significant difference in tolerances.
Explanation:
To test the proper function of the tractor protection valve, a statistical hypothesis test can be performed to compare the pressure tolerances of two different valves. In this scenario, Valve A and Valve B are being compared. We've been given that 15 out of a random sample of 100 of Valve A cracked under 4,500 psi, and 6 out of a random sample of 100 of Valve B cracked under that same pressure. We will use a chi-square test for independence to test at a 5 percent level of significance.
The null hypothesis (H0) is that there is no difference in pressure tolerances between Valve A and Valve B. On the other hand, the alternative hypothesis (Ha) is that there is a difference. The chi-square statistic can be calculated, and compared against critical values from the chi-square distribution to determine if there's significant evidence to reject the null hypothesis.
If the computed p-value is less than the significance level of 0.05, we reject the null hypothesis, indicating that there is a statistically significant difference in pressure tolerances between the two types of valves.
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