Question

according to the us censusbureau in 2009 11% of children in the us live with a grandparent. a recent study of 500 children found that 70% of them live with a parent. at a 2% significant level is, is there enough evidence to suggest the percentage of children in the us who live with a grandparent is different from 11%?

Answer 1

Ho :   p =    0.11  
H1 :   p ╪   0.11   (Two tail test)
          
Level of Significance,   α =    0.02  

Sample Size,   n =    500  
          
Sample Proportion ,    p̂ = 0.70
          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0140  
Z Test Statistic = ( p̂-p)/SE =    (0.7-0.11)/0.014=   42.16  

          
p-Value   =   0.0000   [excel formula =2*NORMSDIST(z)]
Decision:   p-value<α , reject null hypothesis

      
There is enough evidence to  suggest the percentage of children in the us who live with a grandparent is different from 11%       

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