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Sample Proportions

Sample Proportions. AP Stats Section 9.2 . Sample Distributions of a Sample Proportion. Recall notation for a population proportion: p Recall notation for a sample proportion: What is a proportion? A fraction A decimal A percent. Sample Distributions of a Sample Proportion.

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Sample Proportions

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  1. Sample Proportions AP Stats Section 9.2

  2. Sample Distributions of a Sample Proportion • Recall notation for a population proportion: • p • Recall notation for a sample proportion: • What is a proportion? • A fraction • A decimal • A percent

  3. Sample Distributions of a Sample Proportion • What is the goal? • To take many samples to see how well estimates p. • INFERENCE!

  4. Sample Distributions of a Sample Proportion • Some facts to know and use for choosing a sample size n from a large population with p having some characteristic of interest: • Shape: • The sampling distribution of is approximately normal and is closer to normal as n increases. • Mean: • The mean of the sampling distribution is exactly p. • This ensures that is an unbiased estimator of p.

  5. Sample Distributions of a Sample Proportion • Standard Deviation: • The standard deviation of a sampling distribution is • However, this can only be used if the population is large enough. • Most Often Used: • For categorical variables.

  6. The Requirements • What is “large enough?” • Can use if the population is at least 10 times as big as the sample. • What is “approximately normal?” • Can call a distribution normal when: np ≥ 10 and n(1-p) or nq≥ 10 • Why would we want to do that? • To use a z-score and Table A.

  7. New Language and Notation • Read the first paragraph plus one sentence one pg. 474… • First check to make sure we can use our facts. • Check the population size. • Check for normal. • Now solve the problem. • Same thing for pg. 476.

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