The Roper Organization conducted identical surveys in 1995 a

The Roper Organization conducted identical surveys in 1995 and 2005. One question asked women was \"Are most men basically kind, gentle, and thoughtful?\" The 1995 survey revealed that, of the 3,000 women surveyed, 2,010 said that they were. In 2005, 1,530 of the 3,000 women surveyed thought that men were kind, gentle, and thoughtful. At the .05 level, can we conclude that women think men are less kind, gentle, and thoughtful in 2005 compared with 1995?

Z=-12.60 (show all work)

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 =    0.51      
p2 = x2/n2 =    0.67      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.012529964      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -12.76939015      
          
As significance level =    0.05   , then the critical z is  
          
zcrit =    -1.644853627      
          
As |z| > 1.645, then we    REJECT THE NULL HYPOTHESIS.      

There is significant evidence to conclude that women think men are less kind, gentle, and thoughtful in 2005 compared with 1995. [CONCLUSION]