1. Statistical Inference
Introduction to
Statistical Inference

3. 1
We observed !

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

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

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

7. statistic vs. parameter
sample
population
statistic vs. parameter

8. Parameter characterizes the population8

9. Statistic is a function of a sample.

10. Statistic

11. sample mean, sample median & sample variance11

12. (o) 12

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

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

15. 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

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

17. 17

18. 18

19. ?

20. ? 1 2 3 4 5 6
1/6

21. 1 2 3 4 5 6 1 2 3 4 5 6
1.5
2.5
3.5
4.5
5.5

22. Sampling distribution:
the distribution that a statistics follows.

23. 1 2 3 4 5 6
0.00
0.05
0.10
0.15
0.20
0.25
0.30 n = 8

24. 24

25. 25

26. 26

27. 27

28. Why (n-1) ? 28

29. Which one is better ?

30. for large

33. 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

34. unbiased!
unbiased! 34

35. 35

36. biased ! 36

37. unbiased!
unbiased! 37

39. Strong Law of Large Numbers (SLLN)

40. X

41. Central Limit Theorem (CLT)

43. Thank you !!