Asurvey of shoppers is planned to determine what percentage use credit cards. prior surveys suggest 63% 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 4% with 95% confidence?

We would need a sample size of 560.

We first calculate the z-score associated. with this level of confidence:
Convert 95% to a decimal:  95% = 95/100 = 0.95
Subtract from 1:  1-0.95 = 0.05
Divide by 2:  0.05/2 = 0.025
Subtract from 1:  1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this is associated with a z-score of 1.96.

The margin of error, ME, is given by:


We want ME to be 4%; 4% = 4/100 = 0.04.  Substituting this into our equation, as well as our proportion and z-score,

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