Company X is a manufacturer that manufactures expensive computer components. The quality control manager has recently become frustrated with the number of components destroyed during the manufacturing process. He has told the CFO that the average assembly line worker destroys 12 or more components in a single shift. The quality control manager has informed this amount is unacceptable and these assembly line workers should be fired. The CFO is taking this complaint seriously but thinks the number of destroyed items is less than what the quality control manager claims. In order to investigate the quality control manager's claim, the CFO takes a random sample of 15 assembly line employees to see how many components are destroyed by each worker in a single shift. The sample is as follows:

1 14 8 15 17 10 12 6 14 21 15 9 11 4 8

Assuming that the number of destroyed items is normally distributed with a standard deviation of 3, can the CFO infer at the 10% significance level that the average number of destroyed components is less than 12?

Explain. All work must be shown.