Question

A wire manufacturer is very concerned about the consistency of the machines that produce wires and believes that the wires produced by machine A have a smaller variance in diameter than the variance in diameter from machine B. The sample variance of a sample of 16 16 wires from machine A is 0.0461 0.0461 . The sample variance of a sample of 19 19 wires from machine B is 0.0495 0.0495 . Test the claim using a 0.05 0.05 level of significance. Let σ21 σ 1 2 represent the population variance for machine A.

Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer(s) to four decimal places.

Step 3 of 5: Compute the value of the test statistic. Round your answer to four decimal places.

Step 4 of 5: Make a decision.

Step 5 of 5: State the test's conclusion. Does the evidence support the claim?

Answer 1

Step 1:

Null Hypothesis

Alternative Hypothesis

Step 2: Degrees of Frredom = (19-1), (16-1) = (18, 15)

Significance Level  

The Critical value of F for (18,15) df at 5% significance level is 2.3533

Step 3: Under H0, the test statistic is

Step 4: Since calculated value of F is less than critical valaue of F. Fail to REject H0.

Ste5: Hence at 5% significance level, we donot have enough evidence to support the claim that the wires produced by machine A have a smaller variance in diameter than the variance in diameter from machine B