8k-4k+4+7-k =
8k-4k-k+4+7 =
3k+11
Answer:
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Step-by-step explanation:
Answer:
We are given:
![\hat{p}=\frac{278}{700}=0.397](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cfrac%7B278%7D%7B700%7D%3D0.397)
is the critical value at 0.02 significance level
is the margin of error
Therefore, the required sample size is:
![n=\hat{p}(1-\hat{p}) \left(\frac{z_{\frac{0.02}{2}} }{E} \right )^{2}](https://tex.z-dn.net/?f=n%3D%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%20%5Cleft%28%5Cfrac%7Bz_%7B%5Cfrac%7B0.02%7D%7B2%7D%7D%20%7D%7BE%7D%20%5Cright%20%29%5E%7B2%7D)
![=0.397(1-0.397) \left( \frac{2.33}{0.035} \right)^2](https://tex.z-dn.net/?f=%3D0.397%281-0.397%29%20%5Cleft%28%20%5Cfrac%7B2.33%7D%7B0.035%7D%20%5Cright%29%5E2)
![=0.239391 \times 4431.755102](https://tex.z-dn.net/?f=%3D0.239391%20%5Ctimes%204431.755102)
![=1060.922286 \approx 1061](https://tex.z-dn.net/?f=%3D1060.922286%20%5Capprox%201061)
Therefore, the required sample size n = 1061