Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc.(population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length.Recently, Stockton revised its rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.10 with n₁ = 8, and, for Stockton, the results were s₂² = 0.05 with n₂ = 10.Assume that rod lengths are normally distributed in the population.If $\alpha$= 0.05, the critical F value is ___.

Question

Quizplus · Accepted Answer

To compare the variability of two populations, we can use the F-test. In this case, we are testing if the variance of Redding's rods (population 1) is significantly different from the variance of Stockton's rods (population 2). The formula for the F-statistic is:

F = s1^2 / s2^2

where s1 and s2 are the sample standard deviations for populations 1 and 2, respectively.

We are given s1 = 0.10 and s2 = 0.05, along with sample sizes of n1 = 8 and n2 = 10. Plugging these values into the formula above gives:

F = 0.10^2 / 0.05^2 = 4

To determine if this F-statistic is significant, we need to compare it to the critical F-value at a significance level of 0.05 and with degrees of freedom of (n1-1) and (n2-1). From an F-table, we find that the critical F-value for these degrees of freedom is approximately 3.29. Since our calculated F-value (4) is greater than the critical F-value (3.29), we can reject the null hypothesis and conclude that the variance of Redding's rods is significantly different from the variance of Stockton's rods. Therefore, Stockton's revision to their rod shearing operation has made them more competitive with Redding in terms of variability, and Collinsville Construction Company should reconsider purchasing from Stockton.

Collinsville Construction Company Purchases Steel Rods for Its Projects α\alphaα = 005, the Critical F Value Is ___

Collinsville Construction Company Purchases Steel Rods for Its Projects $\alpha$ = 005, the Critical F Value Is ___