Test of Significance: Alkaline Batteries
The reputation (and hence sales) of many businesses can be
severely damaged by shipments of manufactured items that
contain a large percentage of defectives. For example,
a manufacturer of alkaline batteries may want to be reasonably
certain that fewer than 5% of its batteries are defective.
Suppose 300 batteries are randomly selected from a very large
shipment. Each is tested, and 10 defective batteries are
found. Does this provide sufficient evidence for the manufacturer
to conclude that the fraction defective in the entire shipment is
less than 5%?
(Notes:
- Show the P-value to be 0.0885 and draw some conclusion.
- If you don't know what you're doing, try constructing a
80% confidence interval for the proportion of defective
batteries in the shipment.
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