Question

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?

Answer #1

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.

A gigantic warehouse stores approximately
80 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 0.04 with 90% confidence?

A. A gigantic Water Co. warehouse stores approximately 50
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 0.077 with 95% confidence?...

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