6.1 – Gender Selection. The Genetics and IVF Institute conducted a clinical tria

Question

6.1 – Gender Selection. The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to parents using the YSORT method, and 239 of them were boys.

You are given n = 291, x = 239, & confidence level c = 0.99.

a) What is the best point estimate of the population proportion of boys born to parents using the YSORT method? Identify p from the output above.

b) Use the sample data to construct a 99% confidence interval estimate of the proportion of boys born to parents using the YSORT method. From the output above, identify the 99% confidence interval for the population proportion p.

c) Based on the results, does the YSORT method appear to be effective? Why or why not?

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n = 239/291 =   0.821305842   [ANSWER]

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b)      
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.022457486          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.057846651          
lower bound = p^ - z(alpha/2) * sp =   0.763459191          
upper bound = p^ + z(alpha/2) * sp =    0.879152493          
              
Thus, the confidence interval is              
              
(   0.763459191   ,   0.879152493   ) [ANSWER]

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c)

YES, BECAUSE THE WHOLE INTERVAL IS GREATER THAN 0.5, which is the usual probability of conceiving a boy.

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