Download Handout 5

Handout 5
Summary of Chapters 8 and 9.1-3
Sampling Distribution Basic Concepts
 What are we studying here? How statistics vary from sample to sample.
 Why do we study sampling distribution? How good a statistic estimates a parameter?
 Is an estimator biased? Look at the center (mean) of its sampling distribution.
 How precise is an estimator? Look at the variation (standard deviation) of its sampling
distribution.
Sampling Distribution of Sample Proportion p̂
 Unbiased estimator: mean of p̂ equals population proportion p .
 Precision: standard deviation of p̂ (also called standard error, the average difference between
p̂ and p ):

p(1  p )
n
When sample size is sufficiently large, the sampling distribution of p̂ is approximately normal
distribution N ( p,
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
p(1  p)
)
n
Empirical rule for using the normal approximation: np  5 and n(1  p)  5
Use the normal approximation to calculate the probabilities regarding p̂ .
Hypothesis testing: Compute p-values and type I error based on sampling distribution of p̂ .
More inference on Sample Proportion p̂
 Hypothesis testing: know how to set up the null and alternative hypothesis from a story.
 Hypothesis testing: pay attention to the direction of the extremes and how it affects the way Pvalues are obtained.
 Hypothesis testing: follow the procedure in section 9.3; find the test-statistic, then the P-value.
 Draw your conclusion based on the P-value
Sample Distribution of Sample Mean X
 Unbiased:  X  


Standard error:  X 
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When population follows a normal distribution, the sampling distribution of X is normal
Central Limit Theorem: regardless of the population distribution, for sufficient large sample
size (n>30), the sampling distribution of sample mean is approximately normal.
Use the sampling distribution of X to calculated the probabilities
Hypothesis testing: compute p-values and type I error based on the sampling distribution of X .
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n