How to Calculate the Minimum Binomial Sample Size

Instructions

1. • 1

     Identify the following from your question or data:

     zsub(a/2) (The z-value: divide the confidence interval by two and look up the value in the z-table.)
     E (the margin of error)
     Phat (percentage of respondents with positive responses)
     Qhat (1-Phat)

     For example, suppose the question is: "51 percent of residents say they support the local football team. How many residents should you survey with a 95 percent confidence interval 6 percent wide?"
     Your variables would be:

     zsub(a/2)=1.96 (.95/2=0.475. Look up 0.4750 in the z-table: see Resources section)
     E=0.03 (confidence interval of 0.06 divided by two)
     Phat=.51 (percentage of positive respondents expressed as a decimal)
     Qhat=.49 (1-Phat)

   • 2

     Multiply Phat by Qhat. In the above example, .51 x .49 = 0.2499. Set this number aside.

   • 3    Divide zsub(a/2) by E. For the above example, zsub(a/2) divided by E = 1.96 / .03 = 65.3333.

   • 4

     Square Step 3. For our example, 65.333333 x 65.333333 = 4268.444444.

   • 5

     Multiply Step 2 by Step 4. 0.2499 x 4 268.444444 = 1,066.68427. You should survey 1,067 people.