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 it rod shearing operation,and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s₁²= 0.15 with n₁ = 8,and,for Stockton,the results were s₂² = 0.04 with n₂ = 10. Assume that rod lengths are normally distributed in the population If $\alpha$ = 0.05,the observed F value is ___________.

Question

Quizplus · Accepted Answer

The observed F value can be calculated as:

F = s1^2 / s2^2

Where s1 is the sample standard deviation of Redding's rods, s2 is the sample standard deviation of Stockton's rods.

Plugging in the values, we get:

F = 0.15^2 / 0.04^2

F = 14.063

Since n1 = 8 and n2 = 10, the degrees of freedom for the F-test are:

df1 = n1 - 1 = 7

df2 = n2 - 1 = 9

Using a F-distribution table or calculator with df1 = 7 and df2 = 9, and α = 0.05, we find that the critical F-value is 3.75.

Since the observed F-value (14.063) is larger than the critical F-value (3.75), we reject the null hypothesis and conclude that there is significant difference in the variability of rod lengths between Redding and Stockton. Therefore, it is recommended to continue purchasing rods from Redding.

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

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