Mathematics: A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 425 babies were born, and 340 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? 0.75less than pless than 0.85 (Round to three decimal places as needed.) Does the method appear to be effective? No, the proportion of girls is not significantly different from 0.5. Yes,

A clinical trial tests a method designed to increase

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alex24gonzales

22.01.2022

Mathematics

0.75<p<0.85

Yes,the proportion of girls is significantly different from 0.5.

Step-by-step explanation:

We calculate the proportion of girls:

$p=\frac{340}{425}\\\\\\\\=0.8$

#We then calculate the confidence interval as follows:

$CI=p\pm z(ME)\\\\=p\pm z_{0.005}\sqrt{\frac{p(1-p)}{n}}\\\\=0.8+2.576\times \sqrt{\frac{0.8\times 0.2}{425}}\\\\=0.8\pm0.05\\\\=[0.75,0.85]$

Hence, the proportion's confidence interval at 99% is 0.75<p<0.85

#We then state our hypothesis to validate the claim:

$H_o:p=0.5\\H_a:p0.5\\\\p=0.8(True \ mean)$

Since the confidence interval does not contain 0.5, which is the the 50% chance of having a girl, then it can be concluded the proportion of girls is significantly different from 0.5.

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