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# day17 - The Population Proportion The population proportion...

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The Population Proportion The population proportion is p (generally unknown). The sample proportion is ¯ p . We use the sample proportion ¯ p to estimate the population proportion p . Example : In a survey of 1500 American adults released on October 13, 2010, 46% of those questioned said they approved of the job Barack Obama is doing as president. We would also like to make conﬁdence intervals for the population propor- tion. In order to do this, we need to know the sampling distribution of the sample proportion ¯ p . The expected value of the sampling distribution of ¯ p is: The standard error of the sampling distribution of ¯ p is σ ¯ p : The sampling distribution of ¯ p will be approximately normal if np 5 and n (1 - p ) 5 . 1

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Example : A simple random sample of size 100 is selected from a population with p = 0 . 40. a. What is the expected value of ¯ p ? b. What is the standard error of ¯
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day17 - The Population Proportion The population proportion...

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