Answer: 0.0241
Step-by-step explanation:
The formula we use to find the margin of error :
![E=z^*\sqrt{\dfrac{p(1-p)}{n}}](https://tex.z-dn.net/?f=E%3Dz%5E%2A%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
, where z* = Critical value , n= Sample size and p = Sample proportion.
As per given , we have
n= 2400
Sample proportion of subjects showed improvement from the treatment:
![p=\dfrac{720}{2400}=0.3](https://tex.z-dn.net/?f=p%3D%5Cdfrac%7B720%7D%7B2400%7D%3D0.3)
Critical value for 99% confidence = z*= 2.576 (By z-table)
Now , the margin of error for the 99% confidence interval used to estimate the population proportion. :
![E=(2.576)\sqrt{\dfrac{0.3(1-0.3)}{2400}}](https://tex.z-dn.net/?f=E%3D%282.576%29%5Csqrt%7B%5Cdfrac%7B0.3%281-0.3%29%7D%7B2400%7D%7D)
![E=(2.576)\sqrt{0.0000875}](https://tex.z-dn.net/?f=E%3D%282.576%29%5Csqrt%7B0.0000875%7D)
![E=(2.576)(0.00935414346693)](https://tex.z-dn.net/?f=E%3D%282.576%29%280.00935414346693%29)
[Round to the four decimal places]
Hence, the margin of error for the 99% confidence interval used to estimate the population proportion. =0.0241