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

The test statistic for checking the variability (standard deviation or variance) of a population, given a sample, is indeed calculated using the chi-square (χ2) distribution formula: χ2 = (n-1)s^2 / σ^2, where n is the sample size, s is the sample standard deviation, and σ^2 is the population variance. Given the sample standard deviation of 6.7 pounds per square inch and the requirement that the variability not exceed 5 pounds per square inch, the calculation of the test statistic would involve these values, aligning with the provided χ2 value, assuming the correct formula and population variance (σ^2) were used in the calculation.

A Contract Calls for the Strength of a Steel Rod