Answer:
CI=[0.8592,0.9402]
Yes, Method appears to be effective.
Step-by-step explanation:
-We first calculate the proportion of girls born:
[tex]\hat p\frac{x}{n}\\\\=\frac{333}{370}\\\\=0.9[/tex]
Since np[tex]\geq 10[/tex], we assume normal distribution and calculate the 99% confidence interval as below:
[tex]CI=\hat p\pm z\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=0.9\pm2.576\sqrt{\frac{0.9\times 0.1}{370}}\\\\=0.9\pm 0.0402\\\\={0.8598, \ 0.9402][/tex]
Hence, the confidence interval is {0.8598, 0.9402]
-The probability of giving birth to a girl is 0.5 which is less than the lower boundary of the confidence interval, it can be concluded that the method appears to be effective.
