Question

A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.22 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 28 bolts has an average diameter of 0.23cm with a standard deviation of 0.2478. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level?

Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary.

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 to three decimal places.

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

Step 4 of 5: Make the decision.

Step 5 of 5: What is the conclusion?

Answer #1

Step 1

To Test :-

H0 :-

H1 :-

Step 2

( From chi square table )

Step 3

Test Statistic :-

χ^{2} = ( ( 28-1 ) * 0.0614 ) / 0.025

χ^{2} = 66.312

Step 4

Test Criteria :-

Reject null hypothesis if

= 66.312 > 46.963 , hence we reject the null hypothesis

Conclusion :- We Reject H0

Step 5

There is sufficient evidence to support manufacturer's claim that the bolts vary by more than the required variance at α=0.01 level.

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