1. Don’t cry because it is all over, smile because it happened

2. Potential Problems in Sampling Poor Sampling Frame Cost of Sampling Built -In Bias

3. Cost of Sampling Money Time Wide Geographic Region

4. Major Errors in Sampling Bias: Consistent, repeated divergence in the same direction of a sample statistic from its associated population parameter. Lack of Precision: Large theoretical variation in a sample statistic

5. Sampling Error The difference between the sample statistic and its corresponding population parameter. Population: 97, 103, 96, 99, 105 (Mean = 100)

6. Non-Sampling Errors Survey Timing Survey Mode Interviewer – Subject Relationship Survey Topic Question Wording Question Sequence

7. Statistical Significance An observed effect so large that it would rarely occur by chance.

8. Hypothesis Testing What is a Hypothesis? A statement about the value of a population parameter developed for the purpose of testing.

9. Hypothesis Testing What is Hypothesis Testing? A procedure, based on sample evidence and probability theory, used to determine whether the hypothesis is a reasonable statement and should not be rejected or is unreasonable and should be rejected.

10. Hypothesis Testing Examples of hypotheses made about a population parameter are: The mean monthly income for systems analysts is $3,625. Twenty percent of all juvenile offenders are caught and sentenced to prison.

11. Hypothesis Testing Null Hypothesis H 0 : A statement about the value of a population parameter. Alternative Hypothesis H 1 : A statement that is accepted if the sample data provide evidence that the null hypothesis is false.

12. Hypothesis Testing Level of Significance: The probability of rejecting the null hypothesis when it is actually true.

13. Hypothesis Testing Statistical testing is often done by testing a hypothesis that you expect to reject.

14. Null Hypothesis Null Hypothesis H 0 : A statement about the value of a population parameter. Stating the current fact(s).

15. Population

16. Graphic Representation of the Population

17. Alternative Hypothesis Alternative (Research) Hypothesis H 1 : A statement that is accepted if the sample data provide evidence that the null hypothesis is false.

18. Sample

19. Graphic Representation of a Large Sample

20. Graphic Representation of the Population & Sample Sample Z Population Z

21. Statistics! Statistics! Statistics! Finish the Maze and we get to take a break!

22. Testing a Hypothesis Tail

23. Testing a Hypothesis.05 level of significance One tailed test: More than; greater than; larger than; etc… Critical Z 1.645Z Critical Value Critical Region. 05 Area Null Hypothesis Area

24. One Tailed Test,.05 Smaller than; less than, etc. Critical Z 1.645 Z Z value Critical Region Null Hypothesis Area

25. Two Tailed Test,.05 Not Equal to; Different Than Critical Z 1.96 Z Z value 1.96 Z Z value + Critical Region Null Hypothesis Area

26. Graphic Representation of Hypothesis Test Results

27. This maze is longer than I thought. Go Ahead and take a break!

28. Hypothesis Testing State null and alternative hypothesis Select a level of significance Formulate a decision rule Identify the test statistic Take a sample, arrive at a decision (Reject or fail to reject the null)

29. Test for Sample Means X = Sample mean μ = Hypothesized population mean s = Sample standard deviation N = Sample size S

30. One Sample Mean Problem A recent article in Vitality magazine reported that the mean amount of leisure time per week for American men is 40.0 hours. You believe this figure is too large and decide to conduct your own test. In a random sample of 60 men, you find that the mean is 37.8 hours of leisure per week with a standard deviation of 12.2 hours. Can you conclude that the data in the article is too large? Use the.05 significance level.

31. Step 1 State the null and alternative hypothesis. H 0 : Mean = 40.0 hours H 1 : Mean < 40.0 hours

32. Step 2 Select a level of significance. This will be given to you. In this problem, it is.05.

33. Step 3 Establish critical region by converting level of significance to a Z score..5000 -.0500 =.4500 = 1.64z If the test statistic falls below -1.64z, the null hypothesis will be rejected.

34. Step 4 Identify the test statistic. Z = 37.8 – 40.0 12.2 / 7.75 Z = -2.2 / 1.57 Test Statistic: Z = -1.40

35. Step 5 Arrive at a decision. The test statistic falls in the null hypothesis region. Therefore, we fail to reject the null.

36. Test for Two Sample Means X i = Mean for group i S i = Standard deviation for group i n i = Number in group i

37. Two Sample Means Problem The board of directors at the Anchor Pointe Marina is studying the usage of boats among its members. A sample of 30 members who have boats 10 to 20 feet in length showed that they used their boats an average of 11 days last July. The standard deviation of the sample was 3.88 days. For a sample of 40 member with boats 21 to 40 feet in length, the average number of days they used their boats in July was 7.67 with a standard deviation of 4.42 days. At the.02 significance level, can the board of directors conclude that those with the smaller boats use their crafts more frequently?

38. Step 1 State the null and alternative hypothesis. H 0 : Large boat usage = small boat usage H 1 : Smaller boat usage > large boat usage

39. Step 2 Select a level of significance. This will be given to you. In this problem it is.02.

40. Step 3 Formulate a decision rule..5000 -.0200 =.4800 = 2.05z

41. Step 4 Identify the test statistic. 11 – 7.67 = 3.35z 3.88 2 + 4.42 2 30 40

42. Step 5 Arrive at a decision. The test statistic falls in the critical region, therefore we reject the null.

43. p-Value in Hypothesis Testing p-Value: The probability, assuming that the null hypothesis is true, of getting a value of the test statistic at least as extreme as the computed value for the test. If the p-value area is smaller than the significance level, H 0 is rejected. If the p-value area is larger than the significance level, H 0 is not rejected.

44. Statistical Significance p-Value: The probability of getting a sample outcome as far from what we would expect to get if the null hypothesis is true. The stronger that p-value, the stronger the evidence that the null hypothesis is false.

45. Statistical Significance P-values can be determined by - computing the z-score - using the standard normal table The null hypothesis can be rejected if the p- value is small enough.

46. P-Value 1.64 Z 2.05Z