1. 1 Doing Statistics for Business Doing Statistics for Business Data, Inference, and Decision Making Chapter 8 Hypothesis Testing : An Introduction

2. 2 Doing Statistics for Business Chapter 8 Objectives Ü What Is a Hypothesis Test? Ü Overview of Hypotheses to be Tested Ü The Pieces of a Hypothesis Test Ü Two-Tail Tests of the Mean: Large Sample Ü Which Theory Should Go into the Null Hypothesis?

3. 3 Doing Statistics for Business Chapter 8 Objectives (con’t) Ü One-Tail Tests of the Mean: Large Sample Ü What Error Could You be Making?

4. 4 Doing Statistics for Business What is an Hypothesis Test? The word hypothesis has the same meaning in statistics as it does in everyday use. What does this word mean to you? Some possibilities are: m an idea m an assumption m a guess m a theory

5. 5 Doing Statistics for Business In statistics, a Hypothesis is an idea, an assumption, or a theory about the characteristics of one or more populations.

6. 6 Doing Statistics for Business A Hypothesis Test is a statistical procedure that involves formulating a hypothesis and using sample data to decide on the validity of the hypothesis.

7. 7 Doing Statistics for Business The Null Hypothesis is a statement about a parameter of the population(s). It is referred to as H 0. The Alternative Hypothesis is a statement about a parameter of the population(s) that is opposite to the null hypothesis. It is referred to as H A.

8. 8 Doing Statistics for Business A Test Statistic is calculated from the sample data and is used to decide between the null and alternative hypothesis. The rejection region is the range of values of the test statistic that will lead you to reject the null hypothesis. Alpha, , is the area of the rejection region.

9. 9 Doing Statistics for Business 5-Step Hypothesis Testing Procedure Step 1: Set up the null and alternative hypotheses. Step 2: Define the test procedure. This includes selecting the right test, picking the value of , and finding the rejection region. Step 3: Collect the data and calculate the test statistic. Step 4: Decide whether or not to reject the null hypothesis. Step 5: Interpret the statistical decision in terms of the stated problem.

10. 10 Doing Statistics for Business Figure 8.1 Possible Rejection Region

11. 11 Doing Statistics for Business Figure 8.2 Rejection Region for a two-tail test of  -z  z 

12. 12 Doing Statistics for Business The p value is defined to be the smallest value of  for which you can reject H 0.

13. 13 Doing Statistics for Business TRY IT NOW! The Tissue Company Finding the p Value Find the p value for the tissue company’s two-tail test of . Recall that the average MDStrength was found to be 980 lb/ream and the Z statistic was calculated to be -2.40.

14. 14 Doing Statistics for Business A Type I Error is made when you reject the null hypothesis and the null hypothesis is actually true. In other words, you incorrectly reject a true null hypothesis. A Type II Error is made when you fail to reject the null hypothesis and the null hypothesis is false. In other words, you continue to believe a false null hypothesis.

15. 15 Doing Statistics for Business The probability of making a Type I Error is called  (alpha). The probability of making a Type II Error is called  (beta).

16. 16 Doing Statistics for Business A Two-Tail Test of the population mean has the following null and alternative hypotheses: H 0 :  = [a specific number] H A :   [a specific number]

17. 17 Doing Statistics for Business A Lower-Tail Test of the population mean has the following null and alternative hypotheses: H 0 :   [a specific number] H A :  < [a specific number]

18. 18 Doing Statistics for Business An Upper-Tail Test of the population mean has the following null and alternative hypotheses: H 0 :   [a specific number] H A :  > [a specific number]

19. 19 Doing Statistics for Business Summary A Two-Tail Test m Is used to test if the parameter has shifted away from a certain number in either direction, increased or decreased. m Must always be set up so the “=“ theory is the null hypothesis. m Is used when the problem statement has the key words changed or different in the problem statement.

20. 20 Doing Statistics for Business Summary A Lower-Tail Test m Is used to test if the parameter has shifted to a number less than a certain number. m Must always be set up so the “=“ as part of the null hypothesis. m Is used when the problem statement has the key words decreased, reduced, less than. m The theory that you wish to “prove” is placed into the alternative hypothesis.

21. 21 Doing Statistics for Business Summary An Upper-Tail Test m Is used to test if the parameter has shifted to a number more than a certain number. m Must always be set up so the “=“ as part of the null hypothesis. m Is used when the problem statement has the key words increased, greater than. m The theory that you wish to “prove” is placed into the alternative hypothesis.

22. 22 Doing Statistics for Business Figure 8.3 Rejection Region for a two-tail test of  with  = 0.05

23. 23 Doing Statistics for Business Chapter 8 Summary In this chapter you have learned: 4 The key steps in doing any Hypothesis Test begins with formulating two opposing viewpoints called the Null and Alternative Hypotheses. 4 These hypotheses are theories or ideas about the value of one or more population parameters.

24. 24 Doing Statistics for Business Chapter 8 Summary (con’t) 4 The technique of Hypothesis Testing helps you decide between these opposing hypotheses using the sample data as the evidence upon which to base your decision. 4 In doing any hypothesis test there are two possible errors you can make Type I and Type II

25. 25 Doing Statistics for Business Chapter 8 Summary (con’t) 4 The probability of making these errors are labeled  and , respectively. 4 Large Sample Tests are applied whenever you know the population standard deviation or if you have a sufficiently large sample size, n > 30.