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 :

n =89

= 0.348

1 - = 1 - 0.348 = 0.652

At 99.5% confidence level the z is ,

= 1 - 99.5% = 1 - 0.995 = 0.005

/ 2 = 0.005 / 2 = 0.0025

Z/2 = Z0.0025 = 2.810

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

= 2.810 * (((0.348* 0.652) / 89 )

= 0.14

Margin of error = 0.1