Q&A: A manufacturer of plastic bags is ready to make a recall.?

Question by : A manufacturer of plastic bags is ready to make a recall.?

A manufacturer of plastic bags is ready to issue a recall of their product if more than 3.8% of them are defective. They examine 478 of their bags, and of those 478 bags, 12 of them are found to be defective.

What is the test statistic z-value of this study?
Please please please help me i have no idea how to do this!

Best answer:

Answer by Aaron
Well, your sample proportion, p-hat, is 12/478 = .0251.
The z-score for this would be calculated with z = (p-hat – hypothesized p)/(stdev)
The stdev for the sampling distribution of sample proportions is ?((p-hat*q-hat)/n), where q-hat = 1 – p-hat.
So, z = (.0251 – .038)/?((.0251)(.9749)/478) = -1.80

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