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AP Statistics

AP Statistics. Sampling Distributions. Population vs. Sample. A parameter is a number that describes the population. The true value is often unknown because it is difficult to measure the entire population.

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AP Statistics

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  1. AP Statistics Sampling Distributions

  2. Population vs. Sample • A parameter is a number that describes the population. The true value is often unknown because it is difficult to measure the entire population. • A statistic is a number that describes a sample. The value of a statistic is known when we have taken a sample, but it changes from sample to sample. Statistics estimate parameters.

  3. Which is which??? • Determine whether the following are parameters or statistics. • A department store reports that 84% of all customers who use the store’s credit plan pay their bills on time. • A sample of 100 students at a large university had a mean age of 24.1 years. • The Department of Motor Vehicles reports that 22% of all vehicles registered in a particular state are imports. • A hospital reports that based on the 10 most recent cases, the mean length for surgical patients is 6.4 days. • A consumer group, after testing 100 batteries of a certain brand, reported an average life of 63 hours of use.

  4. Notation • Population parameters are written as Greek letters whereas sample statistics are written with English letters. • Mean: μ vs x-bar • St. Dev: σ vs. S • Proportion: p vs p-hat (some books use π (pi))

  5. Statistics: in a nutshell • The rest of the semester we will more or less be trying to convince people that what we observed in our sample can be reasonably used to draw conclusions about the population.

  6. Experiment • How many siblings do each of you have? • Let’s try to estimate the true mean, using a random sample of 5 students.

  7. Sampling Distribution • The distribution that would be formed by considering the value of a sample statistic for every possible sample of a given size from a population is called its sampling distribution.

  8. Sampling Distributions • See pp494-496 ex. 9.5 • Note the shape and center of the sampling distribution. • Note how the sampling distribution changed when the sample size was increased to n = 1000 on p496.

  9. Exercises • p489: 9.1 – 9.4 • p495: 9.7 • P499: 9.8, 9.9 a – e.

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