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Sagot :
Answer: 1068
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Work Shown:
[tex]n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{1.96}{0.03}\right)^2\\\\n \approx 1067.111\\\\n \approx \boldsymbol{1068}\\\\[/tex]
Notes:
- At 95% confidence, the z critical value is roughly z = 1.96 which is determined using a Z table.
- E = 0.03 to represent the 3% error.
- We're not told the value of [tex]\hat{p}[/tex], so we assume the most conservative estimate of 0.5
- Always round up to the nearest integer. The value 1067.111 is closer to 1067, but we round up to 1068 to clear the hurdle needed.
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