Answer:
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:
[tex]p=\frac{340}{425}\\\\\\\\=0.8[/tex]
#We then calculate the confidence interval as follows:
[tex]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][/tex]
Hence, the proportion's confidence interval at 99% is 0.75<p<0.85
#We then state our hypothesis to validate the claim:
[tex]H_o:p=0.5\\H_a:p>0.5\\\\p=0.8(True \ mean)[/tex]
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.
