2. Chapter 18 – Part I Sampling Distribution for Sample Proportion Statistic

3. Review Categorical Variable One Category vs. All Other Categories

4. Examples What political party is the U.S. senator?  Ex. Democrat, All Other Parties Who will you vote for in 2008 election?  Hillary Clinton, All Other Candidates What color are your eyes?  Blue, All Other Eye Colors

5. Review Population characteristics  p = proportion of population members in One Category  1-p = proportion of population members in All Other Categories

6. Examples p = proportion of U.S. senators who are Democrats. p = proportion of voters who will vote for Hillary Clinton. p = proportion of people with blue eyes.

7. Review SRS characteristics  _____ = proportion of sample members in One Category  _____ = proportion of sample members in All Other Categories

8. Examples _____ = proportion of U.S. senators in sample of size 10 who are Democrats. _____ = proportion of voters in sample of size 2000 who will vote for Hillary Clinton. _____ = proportion of people in sample of size 5 with blue eyes.

9. Randomness of Sampling Random event = ___________________. Before taking sample ________________.

10. Repeated Sampling Repeat taking SRS of size n.  Example: 2002 Senate.  ______ = proportion of Democratic Senators in sample of size _______. What happens to values of ________?

11. Repeated Sampling by Hand

12. Repeated Sampling Using Computer

13. Sampling Distribution Many, many possible samples. Many, many possible values of ________. These ___________ are DATA. Summarize DATA values!!

14. Mean (Center)

15. Standard Deviation (Spread)

16. Example 50% of registered voters plan to vote for Hillary Clinton. Select n people. (2, 5, 10, 25) Find sample proportion of registered voters planning to vote for Clinton. Repeat sampling. What does sampling distribution of sample proportion look like?

18. Example 10% of all people are left handed. Select n people. (2, 10, 50, 100) Find sample proportion of left handed people. Repeat sampling. What does sampling distribution of sample proportion look like?

20. Shape Two conditions 1. np and n(1-p) are both larger than 10. 2. sample size n is less than 10% of population size. Shape is approximately a ________________________!!!

21. Sampling Distribution for _____ Check for two conditions

22. Example U.S. Senators Check assumptions (p = 0.54) 1. 10(0.54) = 5.4 and 10(0.46) = 4.6 2. n = 10 is 10% of the population size. Assumption 1 does not hold. Sampling Distribution of ___________

23. Example #1 Public health statistics indicate that 26.4% of the adult U.S. population smoke cigarettes. Describe the sampling distribution for the sample proportion of smokers among a random sample of 50 adults.

24. Example #1 (cont.) Check assumptions 

25. Example #1 (cont.)

26. Example #2 A student in Statistics 101 flipped a fair coin 200 times. What is the sampling distribution of the proportion of heads flipped?

27. Example #2 (cont.) Check assumptions 

28. Example #2 (cont.)

29. Example #3 Information on a packet containing 160 seeds that the germination rate of the seeds is 92%. Assume the seeds are a random collection of all seeds produced. What is the sampling distribution of the proportion of seeds in the packet that will germinate?

30. Example #3 (cont.) Check assumptions 

31. Example #3 (cont.)

32. 68-95-99.7 Rule For all normal distributions  Approx. 68% of all observations are between _________ and __________.  Approx. 95% of all observations are between _________ and __________.  Approx. 99.7% of all observations are between _________ and __________.

33. 68-95-99.7 Rule for Sampling Distribution “all observations” – What does this mean?

34. 68-95-99.7 Rule – Example #1

37. 68-95-99.7 Rule – Example #2

40. 68-95-99.7 Rule – Example #3

43. Using the Sampling Distribution Using the 68-95-99.7 rule, we know what to expect for the values of _______ for a given value of ________. Can we use the normal distribution to find the probability of  Having a __________ value below a certain amount?  Having a __________ value above a certain amount?

44. Example #1 What is the probability of getting a random sample of 50 adults with 18 or more smokers?

45. Example #1

46. Example #2 What is the probability that in flipping a fair coin 200 times, we would get 80 or fewer flips with heads?

47. Example #2

48. Example #3 What is the probability that in a packet of 160 seeds we would see 138 or fewer seeds germinate?

49. Example #3