Understanding Central Limit Theorem: Sampling Distributions & Mean Calculations

1. Chapter SixNormal Curves and Sampling Probability Distributions

2. SECTION 5The Central Limit Theorem

3. The Central Limit Theorem is applied in the following ways:

7. or invert and multiply to get the formula you are to use in this class:

8. To find the probability that a sample mean is within a given interval:

10. Case 1

12. CASE 2

14. Sampling Distribution

15. Example of a Sampling Distribution

16. Constructing a Sampling Distribution of the Mean for Samples of Size n = 2 List all samples and compute the mean of each sample. sample: mean: sample: mean {1,1} 1.0 {1,6} 3.5 {1,2} 1.5 {2,1} 1.5 {1,3} 2.0 {2,2} 2.0 {1,4} 2.5 … ... {1,5} 3.0 How many different samples are there? 36

17. Sampling Distribution of the Mean p 1.0 1/36 1.5 2/36 2.0 3/36 2.5 4/36 3.0 5/36 3.5 6/36 4.0 5/36 4.5 4/36 5.0 3/36 5.5 2/36 6.0 1/36

18. Sampling Distribution Histogram

20. The following are true:

21. We can use this theorem to draw conclusions about means of samples taken from normal distributions.If the original distribution is normal, then the sampling distribution will be normal.

22. The Mean of the Sampling Distribution

23. The mean of the sampling distribution is equal to the mean of the original distribution.

24. The Standard Deviation of the Sampling Distribution

25. The standard deviation of the sampling distribution is equal to the standard deviation of the original distribution divided by the square root of the sample size.

37. 1.

38. 0.33

39. 1.00

40. 2.67

41. 3.33

42. 4.00

44. 2.

45. -0.33 0.17

46. -1.00 0.50

47. -2.67 1.33

48. -3.33 1.67

49. -4.00 2.00