A gigantic warehouse stores approximately 40 million empty aluminum beer and soda cans. Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with blackspot, rendering them unusable. A statistician was hired by the insurance company to estimate p, the true proportion of cans in the warehouse that were contaminated by the fire. How many aluminum cans should be randomly sampled to estimate p to within 0.08 with 90% confidence?
The margin of error we desire is ME = 0.08, and for 90% confidence, we use Z0.05= 1.645 (well-known value using Z table).
Since we have no prior knowledge about the proportion p, we use the conservative estimate of = 0.5.
We have:
So, n =106 aluminum cans should be randomly sampled to estimate p to within 0.08 with 90% confidence.
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