Complete Question 
Country financials, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. In February 2012, a sample of 1000 adults showed 410 indicating that their financial security was more that fair. In Feb 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair.
a
State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b
What is the sample proportion indicating that their  financial security was more that fair in 2012?In 2010?
c
Conduct the hypothesis test and compute the p-value.At a .05 level of significance what is your conclusion?
Answer:
a
The null hypothesis is  
The  alternative hypothesis is   
b
in 2012  
in 2010   
   
c
The  p-value  is  
The conclusion is 
There is  sufficient evidence to conclude that the proportion of those indicating that  financial security is more fair in Feb 2010 is different from the proportion of  those indicating that financial security is more fair in Feb 2012.
Step-by-step explanation:
From the question we are told that 
    The  sample size in 2012 is  
     The  number that indicated that their finance was more than fail is  k  =  410  
      The  sample  size in 2010  is   
 
    The  number that indicated that their finance was more than fail is  u  =  315
      The  level of significance is  ![\alpha  =  0.05[/ex]The null hypothesis is  [tex]H_o :  p_1 = p_2](https://tex.z-dn.net/?f=%20%5Calpha%20%20%3D%20%200.05%5B%2Fex%5D%3C%2Fp%3E%3Cp%3EThe%20null%20hypothesis%20is%20%20%5Btex%5DH_o%20%3A%20%20p_1%20%3D%20p_2)
The  alternative hypothesis is   
Generally the sample proportion for  2012 is mathematically represented as 
      
=>   
=>   
Generally the sample proportion for  2010 is mathematically represented as 
       
=>   
=>    
    
Generally the pooled sample proportion is mathematically represented as 
       
=>     
=>      
Generally the test statistics is mathematically represented as 
      
   
     
  
   
 
    
Generally the p- value  is mathematically represented as  
       
From the z -table  
        
 
So  
       
         
So from the p-value  obtained we see that p-value  <   so we reject the null hypothesis
 so we reject the null hypothesis 
 Thus there is  sufficient evidence to conclude that the proportion of financial security is more fair in Feb 2010 is different from the proportion of financial security is more fair in Feb 2012.