A contract calls for the strength of a steel rod to stand up to pressure of 200 lbs per square inch on average.The contract also requires that the variability in strength for individual steel rods be no more than 5 pounds per square inch.If a random sample of n = 15 rods is selected and the sample standard deviation is 6.7 pounds,the test statistic is approximately χ² = 25.138.

Question

Quizplus · Accepted Answer

This is a chi-square goodness-of-fit test with one degree of freedom. The calculated test statistic of 25.138 is greater than the critical value at the 0.05 level of significance, indicating that there is significant variability in the strength of the steel rods beyond what is allowed by the contract. Therefore, the null hypothesis (that the variability in strength is no more than 5 pounds per square inch) is rejected.

A Contract Calls for the Strength of a Steel Rod