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A political interest group wants to determine what fraction p ∈ (0, 1) of the population intends to vote for candidate A in the next election. 1000 randomly chosen individuals are polled. 457 of these indicate that they intend to vote for candidate A. Find the 95% confidence interval for the true fraction p.

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Answer:

95% confidence interval for the true fraction p is (0.426, 0.488)

Step-by-step explanation:

Confidence Interval can be calculated using p±ME where

  • p is the sample proportion ([tex]\frac{457}{1000} =0.457[/tex]
  • ME is the margin of error from the mean

and margin of error (ME) around the mean can be found using the formula

ME=[tex]\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} }[/tex] where

  • z is the corresponding statistic in 95% confidence level (1.96)
  • p is the sample proportion (0.457)
  • N is the sample size (1000)

then ME=[tex]\frac{1.96*\sqrt{0.457*0.543}}{\sqrt{1000} }[/tex] ≈ 0.031

Then 95% confidence interval would be 0.457±0.031 or (0.426, 0.488)

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