Question

Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E.that corresponds to a sample of size 89 with 34.8% successes at a confidence level of 99.5%.

M.E. = %

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. Round final answer to one decimal place

Answer 1

Solution :

Given that,

n = 89

= 0.348

1 - = 1 - 0.348 = 0.652

At 99.5% confidence level

= 1 - 99.5%

=1 - 0.99.5 = 0.005

/2 = 0.0025

Z/2 = Z0.0025 = 2.807

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.807(((0.348 * 0.652) / 89 )

= 0.142

Margin of error = E = 14.2%