Please explain equations ThanksSolutionFormulating the hypot

Please explain equations. Thanks.

Solution

Formulating the hypotheses          
Ho: p1 - p2   <=   0  
Ha: p1 - p2   >   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 = 30/120 =   0.25      
p2^ = x2/n2 = 21/100 =   0.21      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.056758259      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    0.704743248      
          
As significance level =    0.05   , then the critical z is  
          
zcrit =    1.644853627      
          
Also, the p value is          
          
P =    0.240485016      
          
As z < 1.645, and P > 0.05, then we    FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that there is a higher proportion of U.S. companies offering high-deductible health insurance plans to their workers in 2006 than in 2005. [CONCLUSION]