Answer:
The sample should be 1,068.
Step-by-step explanation:
Consider the provided information.
Confidence level is 95% and margin of error is 0.03.
Thus,
1-α=0.95
α=0.05, E=0.03 and planning value ![\hat p=0.5](https://tex.z-dn.net/?f=%5Chat%20p%3D0.5)
Formula to calculate sample size is: ![n=\frac{\hat p(1-\hat p)(z_{\alpha/2})^2}{E^2}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%28z_%7B%5Calpha%2F2%7D%29%5E2%7D%7BE%5E2%7D)
From the table we can find:
![z_{\alpha/2}=z_{0.05/2}\\z_{0.025}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.05%2F2%7D%5C%5Cz_%7B0.025%7D%3D1.96)
Substitute the respective values in the above formula we get:
![n=\frac{0.5(0.5)(1.96)^2}{(0.03)^2}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B0.5%280.5%29%281.96%29%5E2%7D%7B%280.03%29%5E2%7D)
![n=\frac{0.25(1.96)^2}{(0.03)^2}\approx 1067.111](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B0.25%281.96%29%5E2%7D%7B%280.03%29%5E2%7D%5Capprox%201067.111)
Hence, the sample should be 1,068.