Question

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 200 comma 90 % confidence The margin of error Eequals nothing. ​(Round to four decimal places as​ needed.)

Answer 1

SOLUTION:

From given data,

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 200 comma 90 % confidence The margin of error Eequals nothing. ​(Round to four decimal places as​ needed.)

Where,

x = 200

n = 500

= x / n = 200 / 500 = 0.4

90% confidence interval

Confidence interval is 90%

90% = 90/100 = 0.90

= 1 - Confidence interval = 1-0.90 = 0.10

/2 = 0.10 / 2

= 0.05

Z_/2 = Z_0.05 = 1.645

The margin of error

The margin of error = Z_/2 * sqrt((1-) / n )

The margin of error = 1.645 * sqrt(0.4(1-0.4) / 500 )

The margin of error = 1.645 * 0.0219089023

The margin of error = 0.0360