Statistical Inference Introduction to Statistical Inference

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1 We observed !

What is the true value of p , in the experiment ? Is exact value of ? No

Plausible range that will be in ? (0, 1) : true but no meaning A reasonable way is . How to take the value ?

Is the statement right ? How can we decide the answer ?

statistic vs. parameter sample population statistic vs. parameter

Parameter characterizes the population 8

Statistic is a function of a sample.

Statistic

sample mean, sample median & sample variance 11

(o) 12

(X) is neither parameter nor statistic (X) (o) 13

non-parametric question vs. parametric question What is the population ? What is and ? non-parametric question vs. parametric question 14

Answer the following questions by using the information obtained from the sample. A: What is ? B: What is the plausible range for ? C: Is true ? 15

We have a random sample obtained from . What is ? estimator 16

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18

?

? 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1/6

1 2 3 4 5 6 1 2 3 4 5 6 1.5 2.5 3.5 4.5 5.5

Sampling distribution: the distribution that a statistics follows. 1 2 3 4 5 6

1 2 3 4 5 6 0.00 0.05 0.10 0.15 0.20 0.25 0.30 n = 8

24

25

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Why (n-1) ? 28

Which one is better ?

for large

For an estimator, if the mean of the sampling distribution of the estimator is equal to the parameter, then the estimator is called unbiased; otherwise biased. 33

unbiased! unbiased! 34

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biased ! 36

unbiased! unbiased! 37

Strong Law of Large Numbers (SLLN)

X

Central Limit Theorem (CLT)

Thank you !!