Question

Country Financial, a financial services company, uses surveys of adults age and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of adults showed indicating that their financial security was more than fair. In February of 2010, a sample of adults showed indicating that their financial security was more than fair. What is the p value

Answer 1

Complete question is;

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 the p value?

Answer:

p-value = 0.006934

Step-by-step explanation:

First of let's define the hypotheses.

Null hypothesis: H0: p1 - p2 = 0

Alternative hypothesis: Ha: p1 - p2 ≠ 0

We are given;

Number of people in 2012 that indicated their financial security was more than fair; x1 = 410

Number of people in 2010 that indicated their financial security was more than fair; x2 = 315

Sample in 2012; n1 = 1000

Sample in 2010; n2 = 900

proportion of people in 2012 that indicated their financial security was more than fair; p1 = x1/n1 = 410/1000 = 0.41

proportion of people in 2010 that indicated their financial security was more than fair; p2 = x2/n2 = 315/900 = 0.35

Now, let's find the z - score with the formula;

z = (p1 - p2)/√[(p1(1 - p1) × (1/n1)) + (p2(1 - p2) × (1/n2))]

Thus;

z = (0.410 - 0.35)/√[(0.41(1 - 0.41) × (1/1000)) + (0.35(1 - 0.35) × (1/900))]

z = 0.06/√0.00049467778

z ≈ 2.7

From online p-value calculator attached using z-value = 2.7; two tailed distribution; significance level = 0.05;

We have; p-value = 0.006934