Question

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: eight percentage points; confidence level 95%; from a prior study, p hat is estimated by the decimal equivalent of 32%

Answer #1

Solution:

Given that,

= 32% = 0.320

1 - = 1 - 0.320 = 0.680

margin of error = E = 8% = 0.08

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2} = Z_{0.025} =
1.960

Sample size = n = ((Z_{ / 2}) / E)^{2} *
* (1 - )

= (1.960 / 0.08)^{2} * 0.320 * 0.680

= 146.9412

= 147

n = sample size = 147

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