Answer:
188 weeks of data must be sampled.
Step-by-step explanation:
From the information given, we can deduce that:
The Margin of error is within = 200
The confidence interval = 95%
The level of significance = 1 - C.I
= 1 - 0.95
= 0.05
The standard deviation = 1400
The number of weeks the data must be sampled can be determined by using the formula for sample size which is:
![n =( \dfrac{Z_{\alpha/2} \times \sigma}{E} )^2](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cdfrac%7BZ_%7B%5Calpha%2F2%7D%20%5Ctimes%20%5Csigma%7D%7BE%7D%20%29%5E2)
![n =( \dfrac{Z_{0.05/2} \times 1400}{200} )^2](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cdfrac%7BZ_%7B0.05%2F2%7D%20%5Ctimes%201400%7D%7B200%7D%20%29%5E2)
![n =( \dfrac{1.96 \times 1400}{200} )^2](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cdfrac%7B1.96%20%5Ctimes%201400%7D%7B200%7D%20%29%5E2)
![n =( \dfrac{2744}{200} )^2](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cdfrac%7B2744%7D%7B200%7D%20%29%5E2)
![n =( 13.72)^2](https://tex.z-dn.net/?f=n%20%3D%28%2013.72%29%5E2)
n = 188.24
n ≅ 188
Thus, 188 weeks of data must be sampled.