Question

3. An article in a journal claims that 37% of American fathers take no responsibility for child care. Using P-value approach and a 0.10 significance level, test the claim using a random sample of 254 fathers, of which 82 did not help with child care.

a. P-value = 0.059; reject H0

b. P-value = 0.940; reject H1

c. P-value = 0.119; fail to reject H0

d. P-value = 0.119; reject H0

e. P-value = 0.059; fail to reject H0

f. P-value = 0.940; fail to reject H1

Answer 1

Null hypothesis          

       
                  
Alternative hypothesis             

   
                  
We have for given example,                  
Population proportion value is =0.37              
x=82              
                  
n=254              
Level of significance =   0.1              
Estimate for sample proportion =0.3228              
                  
Z test statistic formula for proportion                  


=-1.56  

P value = 0.119.......................by using Z table or Excel command =2*NORMSDIST(-1.56)

c. P-value = 0.119; fail to reject H0