A student doing her research on the amount of government expenditure on differen

Question

A student doing her research on the amount of government expenditure on different programs wanted to know if Americans are aware that social security and Medicare takes almost 60% of the total government expenditure. She knows that about 29% of the population knows this from previous studies. She needs to collect a sample to confirm if this is still true at the 95% level of confidence, she also wants her sampling error to be equivalent to 2.5%. How large a sample does she need to achieve this level of accuracy?

Explanation / Answer

Population knows = 29% = 0.29 = p

Zc = 95% = 1.96

Sampling error = 2.5% = 0.025

Sample size = p(1-p) (zc/E)^2

= (0.29)(1-0.29)( 1.96 / 0.025)^2 = 1266

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