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
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