Question

Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February of 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair. At 99% confidence, what is the margin of error? Round to 2 decimal places.

Answer 1

Solution :

Given that,

n = 900

x = 315

Point estimate = sample proportion = = x / n = 0.35

1 - = 0.65

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 * (((0.35 * 0.65) / 900)

= 0.04

The margin of error is 0.04.