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# handout_8_1 - 8.1 recall from 5.1 when n is large Inference...

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8.1 Inference for a Single Proportion recall from 5.1, when n is large: p ˆ ~ N (p, n p p ) 1 ( - ) Large-sample confidence interval for a population proportion Choose an SRS of size n from a large population with unknown proportion p of successes. The sample proportion is: p ˆ = n X where X is the number of successes. The standard error of p ˆ is: p SE ˆ = n p p ) ˆ 1 ( ˆ - and the margin of error for confidence level C is: m =( z *)( p SE ˆ ) where z * is the value for the standard normal density curve with area C between – z * and z *. A approximate level C confidence interval for p is p ˆ ± m Use this interval for 90%, 95%, or 99% confidence when the number of successes and the number of failures are both at least 15.

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Example 1 USA Today polled registered voters in the US and asked, “Do you support President Obama?” Of the 1000 individuals who were polled, 620 responded, “Yes.” Compute the 95% confidence interval for p , the proportion of all registered voters in the US who support President Obama. Large-sample significance test for a population proportion Draw an SRS of size n from a large population with unknown proportion p of successes.
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handout_8_1 - 8.1 recall from 5.1 when n is large Inference...

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