Question

Assume that a random sample is used to estimate a population proportion p. Find the margin...

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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