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.

What is a 95% confidence interval estimate of the difference between the proportions at the two years, 2012 and 2010?

Group of answer choices

A.(LCL, UCL) = (0.81, 7.11)

B.(LCL, UCL) = (2.08, 5.84)

C.(LCL, UCL) = (1.49, 6.43)

D.(LCL, UCL) = (2.38, 5.54)

Answer 1

Given that,

For February of 2012 : n1=1000, x1=410 and

For February of 2010 : n2 = 900, x2 = 315 and

A 95% confidence level has significance level of 0.05 and critical value is,

The margin of error (E) is,

The 95% confidence interval for (p1 - p2) is,

Therefore, a 95% confidence interval estimate of the difference between the proportions at the two years, 2012 and 2010 is (0.0164, 0.1036).

Note : if you want answer rounded to two decimal places then required confidence interval is, (0.02, 0.10)