A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 320 babies were? born, and 288 of them were girls. Use the sample data to construct a 99?% confidence interval estimate of the percentage of girls born. Based on the? result, does the method appear to be? effective?

<p< round to three decimal places

 We are 99% confident that the true value of the population proportion of girls born  lies in the interval  

                                                                     0.857<p<0.943

      Based on these results we can conclude that the method appears to be effective.

Step-by-step explanation

The confidence interval for the population proportion is 

                        [p^?−Zα/2?np^?(1−p^?)??,p^?+Zα/2?np^?(1−p^?)??]

The sample proportion is 

                     p^?=nx?=320288?=0.9

For a 99% confidence interval, α=0.01 and Zα/2?=Z0.01/2?=Z0.005?=2.5758

[0.9−2.57583200.9(1−0.9)??,0.9+2.57583200.9(1−0.9)??]=[0.9−0.04319748,0.9+0.04319748]=[0.8568025,0.9431975]

            We are 99% confident that the true value of the population proportion of girls born  lies in the interval  

                                                                     0.857<p<0.943

      Based on these results we can conclude that the method appears to be effective. these