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Inference on Proportions

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Assumptions: SRS Normal distribution np > 10 & n(1-p) > 10 Population is at least 10n

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Formula for Confidence interval: Normal curve Note: For confidence intervals, we DO NOT know p – so we MUST substitute p-hat for p in both the SD & when checking assumptions.

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A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.

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Assumptions: Have an SRS of adults np =1012(.38) = 384.56 & n(1-p) = 1012(.62) = 627.44 Since both are greater than 10, the distribution can be approximated by a normal curve Population of adults is at least 10,120. We are 95% confident that the true proportion of adults who believe in ghost is between 35% and 41%. Step 1: check assumptions! Step 2: make calculations Step 3: conclusion in context

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Another Gallop Poll istaken in order to measure the proportion of adults who approve of attempts to clone humans. What sample size is necessary to be within + 0.04 of the true proportion of adults who approve of attempts to clone humans with a 95% Confidence Interval? To find sample size: However, since we have not yet taken a sample, we do not know a p-hat (or p) to use!

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What p-hat (p) do you use when trying to find the sample size for a given margin of error?.1(.9) =.09.2(.8) =.16.3(.7) =.21.4(.6) =.24.5(.5) =.25 By using.5 for p-hat, we are using the worst- case scenario and using the largest SD in our calculations.

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Another Gallop Poll is taken in order to measure the proportion of adults who approve of attempts to clone humans. What sample size is necessary to be within + 0.04 of the true proportion of adults who approve of attempts to clone humans with a 95% Confidence Interval? Use p-hat =.5 Divide by 1.96 Square both sides Round up on sample size

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Chapter 8: Estimating with Confidence

Chapter 8: Estimating with Confidence

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