A manufacturer believes that if routine maintenance (cleaning and oiling of machines) is increased to once a day rather than once a week, the number of defective parts produced by the machines will decrease. Nine machines are selected, and the number of defective parts produced over a 24-hour operating period is counted. Maintenance is then increased to once a day for a week, and the number of defective parts each machine produces is again counted over a 24-hour operating period. The data are shown here. At α = 0.01, can the manufacturer conclude that increased maintenance reduces the number of defective parts manufactured by the machines?

Perform these steps.
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified.

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Machine 1 2 3 4 5 6 7 8 9 Before After 6 18 5 4 16 13 20 9 3 5 16 7 4 18 12 14 7 1