Assume that a method of gender selection is being tested wit

Assume that a method of gender selection is being tested with couples wanting to have baby girls. Identify the null hypothesis, alternative hypothesis, test statistic, p-value or critical value(s). Conclusion about the null hypothesis, and final conclusion that addresses the original claim.

Gender selections: Among 100 babies born to 100 couples using a gender-selection method, 55 of them are girls. Use a 0.01 significance level to test the claim that for couples using this method, the proportion of girls is not equal to 0.5.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5 [HYPOTHESES]
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As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.55      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.05      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1 [TEST STATISTIC]

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As this is a    2   tailed test, then, getting the p value,  
          
p =    0.317310508 [P VALUE]

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significance level =    0.01  
  
Comparing P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the method selection alters the probability of a girl from 0.5. [CONCLUSION]