Question

A company manufacturing coffee beans finds that 8% of all beans manufactured are defective. Management is concerned that poorly trained employees is partially responsible for the high defect rate. In an effort to decrease the percentage of defective beans, management decides to provide additional training to employees. After training was implemented, a sample of 450 beans revealed only 27 defects. Was the additional training effective in lowering the defect rate?


At α = 0.01,

		we can conclude that the additional training significantly increased the defect rate.
		we can conclude that the additional training did not significantly lower the defect rate.
		we can conclude that the additional training did not affect the defect rate.
		we can conclude that the additional training significantly lowered the defect rate.
		No conclusion can be made with the given information.

Answer 1

given data are:-

sample size (n) = 450

sample proportion () = 27/450 = 0.06

hypothesis:-

test statistic be:-

p value :-

[using normal table]

decision:-

p value = 0.0594 > 0.01 (alpha)

so, we fail to reject the null hypothesis.

conclusion:-

at alpha = 0.01, we can conclude that the additional training did not significantly lower the defect rate.

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