An article in a journal reports that 34 of American fathers

An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 234 fathers from Littleton yielded 96 who did not help with child care. Test the researcher\'s claim at the 0.05 significance level. Calculate the test statistic z.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.34
Ha:   p   >   0.34
As we see, the hypothesized po =   0.34      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.41025641      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.030967311      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.268728142   [ANSWER, TEST STATISTIC]

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As this is a    1   tailed test, then, getting the p value,  
          
p =    0.011642432      
significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.

Thus, there is significant evidence that the proportion of fathers who take no responsibility in child care is greater for fathers in the town of Littleton. [CONCLUSION]