Chapter 9

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# Chapter 9 - PowerPoint PPT Presentation

Chapter 9. Section 9.1 – Sampling Distributions. Introduction. The process of statistical inference involves using information from a sample to draw conclusions about a wider population.

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### Chapter 9

Section 9.1 – Sampling Distributions

Introduction
• The process of statistical inference involves using information from a sample to draw conclusions about a wider population.
• Different random samples yield different statistics. We need to be able to describe the sampling distribution of possible statistic values in order to perform statistical inference.
• We can think of a statistic as a random variable because it takes numerical values that describe the outcomes of the random sampling process. Therefore, we can examine its probability distribution using what we learned in Chapter 7
Parameters and Statistics
• As we begin to use sample data to draw conclusions about a wider population, we must be clear about whether a number describes a sample or a population.

Remember s and p:

statistics come from samples and

parameters come from populations

• See examples 9.1 & 9.2 on p.488-489
Sampling Variability
• How can be an accurate estimate of ? After all, different random samples would produce different values of .
• This basic fact is called sampling variability: the value of a statistic varies in repeated random sampling.
• To make sense of sampling variability, we ask, “What would happen if we took many samples?”
• See example 9.3 on p.490
Sampling Distribution
• The following diagram represents the distribution of the sample proportion from 1000 SRSs of size 100 drawn from a population with p = 0.7.
• Strictly speaking, the sampling distribution is the ideal pattern that would emerge if we looked at all possible samples of the same size from the population. A fixed number, like the 1000 trials in the figure above is only an approximation to the sampling distribution.
Describing Sampling Distributions
• Describe the shape, center, spread, and any outliers of a sampling distribution to help answer the question, “How trustworthy is a statistic as an estimator of the parameter?”
• See example 9.5 on p.494-495
• The overall shape of the distribution is

symmetric and approximately normal

• The center of the distribution is very

close to the true value of p = .37 for the

population from which samples were drawn.

• The values of have a large spread ranging from .22 to .54. Because the distribution is close to normal we can use standard deviation to describe the spread, which is about .05
• There are no outliers or other important deviations from the overall pattern.

This sampling distribution represents