The genetics & IVF institute conducted a clinical trial of the XSORT method desi

Question

The genetics & IVF institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl. As of this writing, 945 babies were born to process using the XSORT method, and 879) of them were girls. a. What is the best point estimate of the population proportion of girls born to parents using the XSORT method? b. Use the sample data to construct a 95% confidence interval estimate of the proportwnoi of girls born to parents using the XSORT method. c. Based on the results, does the XSORT method appear to be effective? Why or why not?

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    879/945 = 0.93015873   [ANSWER]

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b)      
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.008291225          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.016250502          
lower bound = p^ - z(alpha/2) * sp =   0.913908228          
upper bound = p^ + z(alpha/2) * sp =    0.946409232          
              
Thus, the confidence interval is              
              
(   0.913908228   ,   0.946409232   ) [ANSWER]

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c)

Yes, as this interval is totally greater than 0.50, which is the expected probability of a girl. [ANSWER]

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