1. Chapter 7 Introduction to Sampling Distributions

2. Hmm…déjà vu? 0 Statistic is a numerical descriptive measure of a sample 0 Parameter is a numerical descriptive measure of a population

3. So…let’s do this 0 What are the symbols for Statistic mean, variance, standard deviation?

4. Something new

5. Note: 0 We are going from raw data distribution to a sampling distribution

6. Note #2: 0 We often do not have access to all the measurements of an entire population because of constraints on time, money, or effort. So we must use measurements from a sample.

7. Type of inferences 0 1) Estimation: In this type of inference, we estimate the value of a population parameter 0 2) Testing: In this type of inference, we formulate a decision about the value of a population parameter 0 3) Regression: In this type of inference, we make predictions or forecasts about the value of a statistical variable

8. Sampling distribution 0 It is a probability distribution of a sample statistic based on all possible simple random samples of the same size from the same population

9. Group Work: 0 1) What is population parameter? Give an example 0 2) What is sample statistic? Give an example 0 3) What is a sampling distribution?

10. Answer 0 1) Population parameter is a numerical descriptive measure of a population 0 2) A sample statistic or statistic is a numerical descriptive measure of a sample 0 3) A sampling distribution is a probability distribution for the sample statistic we are using

11. Read page 295-298

12. Homework Practice 0 Pg 298-299 #1-9

13. Central Limit Theorem

15. Note:

16. Example

17. Answer

18. Group Work

19. Standard error

21. Group Work: Central Limit Theorem 0 A) Suppose x has a normal distribution with population mean 18 and standard deviation 3. If you draw random samples of size 5 from the x distribution and x bar represents the sample mean, what can you say about the x bar distribution? How could you standardize the x bar distribution? 0 B) Suppose you know that the x distribution has population mean 75 and standard deviation 12 but you have no info as to whether or not the x distribution is normal. If you draw samples of size 30 from the x distribution and x bar represents sample mean, what can you say about the x bar distribution? How could you standardize the x bar distribution? 0 C) Suppose you didn’t know that x had a normal distribution. Would you be justified in saying that the x bar distribution is approximately normal if the sample size were n=8?

22. Answer

23. Note: 0 A sample statistic is unbiased if the mean of its sampling distribution equals the values of the parameter being estimated 0 The spread of the sampling distribution indicates the variability of the statistic. The spread is affected by the sampling method and the sample size. Statistics from larger random samples have spread that are smaller.

24. Read 304 and 305

25. Homework Practice 0 Pg 306-308 #1-18 eoe

26. Sampling Distributions for Proportions

27. Think Back to Section 6.4 0 We dealt with normal approximation to the binomial. 0 How is this related to sampling distribution for proportions? 0 Well in many important situations, we prefer to work with the proportion of successes r/n rather than the actual number of successes r in binomial experiments.

29. Standard Error

30. Where do these formula comes from?

32. Example:

33. Answer

34. Group Work

35. Word Problem

36. Answer

37. Group work 0 In the OC, the general ethnic profile is about 47% minority and 53% Caucasian. Suppose a company recently hired 78 people. However, if 25% of the new employees are minorities then there is a problem. What is the probability that at most 25% of the new fires will be minorities if the selection process is unbiased and reflect the ethnic profile? (Follow the last example’s footstep)

38. Answer

39. Remember Control Chart? 0 Sketch how a control chart looks like

40. P-Chart 0 It is just like the control chart

41. How to make a P-Chart?

42. Example situation: 0 Civics and Economics is taught in each semester. The course is required to graduate from high school, so it always fills up to its maximum of 60 students. The principal asked the class to provide the control chart for the proportion of A’s given in the course each semester for the past 14 semesters. Make the chart and interpret the result.

43. Example: Semester1234567 r=#of A’s9128156713.15.20.13.25.1.12.22 Semester891011121314 r=#of A’s71198211110.12.18.15.13.35.18.17

44. Answer

45. Group Work 0 Mr. Liu went on a streak of asking 30 women out a month for 11 months. Complete the table and make a control chart for Mr. Liu and interpret his “game”. month1234567 r=says yes10131512205 month891011 r=says yes28723

46. Homework Practice 0 P317-320 #1-13 eoo