Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. n equals 500 comma x equals 350 comma 95 % confidence The margin of error Eequals nothing. (Round to four decimal places as needed.)
Solution :
Given that,
n = 500
x = 350
Point estimate = sample proportion = = x / n = 350 / 500 = 0.700
1 - = 1 - 0.700 = 0.3
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.96 * (((0.700 * 0.3) / 500)
= 0.0402
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