A survey of shoppers is planned to see what percentage use credit cards.Prior surveys suggest 56% of shoppers use credit cards.How many randomly selected shoppers must we survey in order to estimate the proportion of shoppers who use credit cards to within 1% with 95% confidence?

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To determine the sample size needed for estimating a proportion with a specific margin of error and confidence level, we use the formula: n = (Z^2 * p * (1-p)) / E^2. For 95% confidence, Z is 1.96. Given p = 0.56 and E = 0.01, the calculation results in approximately 9466.

A Survey of Shoppers Is Planned to See What Percentage