The IRS is conducting a study to determine the percentage of United States indiv

Question

The IRS is conducting a study to determine the percentage of United States individual taxpayers who overpaid their taxes and received a tax refund for 2009. In a random sample of 2500 individual 2009 taxpayer returns, the IRS found that 1750 were issued refunds.
Show mathematical evidence that the sample size is "large;" that is, that it is large enough to assume that the Central Limit Theorem applies and the the Z Standard Normal table can be appropriately used for the construction of the confidence interval.

Explanation / Answer

We need to check that np>10 and nq > 10 in order to use the normal approximation. Here np = 1750 > 10 and nq = (2500-1750) = 750 > 10, so we're fine.

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