1. © 2001 Prentice-Hall, Inc.Chap 9-1 BA 201 Lecture 15 Test for Population Mean Known

2. © 2001 Prentice-Hall, Inc. Chap 9-2 Topics Z Test for the Mean ( Known) Critical Value Approach to Hypothesis Testing p-Value Approach to Hypothesis Testing

3. © 2001 Prentice-Hall, Inc. Chap 9-3 Example: Two-Tail Test Q. Does an average box of cereal contain 368 grams of cereal? A random sample of 25 boxes showed = 372.5. The company has specified  to be 15 grams and the distribution to be normal. Test at the   0.05 level. 368 gm.

4. © 2001 Prentice-Hall, Inc. Chap 9-4 General Steps in Hypothesis Testing 1. State the H 0 2. State the H 1 3. Choose  4. Choose n 5. Choose Test 6. Set up critical value(s) Reject H 0 -1.96 Z +1.96 Reject H 0 0

5. © 2001 Prentice-Hall, Inc. Chap 9-5 (continued) General Steps in Hypothesis Testing 7. Collect data 8. Obtain test statistic and p-value 9. Make statistical decision 10. Express conclusion

6. © 2001 Prentice-Hall, Inc. Chap 9-6  = 0.05 n = 25 Critical Value: ±1.96 Example Solution: Two-Tail Test Test Statistic: Decision: Conclusion: Do Not Reject at  =.05 No Evidence that True Mean is Not 368 Z 0 1.96.025 Reject -1.96.025 H 0 :  368 H 1 :  368 1.5 0 372.5

7. © 2001 Prentice-Hall, Inc. Chap 9-7 PHStat | One-Sample Tests | Z Test for the Mean, sigma known … Example in Excel Spreadsheet Two-tail Z Test for Mean ( Known) in PHStat

8. © 2001 Prentice-Hall, Inc. Chap 9-8 Critical Values Approach to Testing Convert Sample Statistic (e.g. ) to Test Statistic (e.g. Z, t or F –statistic) Obtain Critical Value(s) for a Specified from a Table or Computer If the test statistic falls in the critical region, reject H 0 Otherwise do not reject H 0

9. © 2001 Prentice-Hall, Inc. Chap 9-9 p-Value Approach to Testing Convert Sample Statistic (e.g. ) to Test Statistic (e.g. Z, t or F –statistic) Obtain the p-value from a table or computer p-value: Probability of obtaining a test statistic more extreme ( or ) than the observed sample value given H 0 is true Called observed level of significance Largest value of that an H 0 will not be rejected Compare the p-value with If p-value, do not reject H 0 If p-value, reject H 0

10. © 2001 Prentice-Hall, Inc. Chap 9-10 p-Value Solution (p Value = 0.1336)  (  = 0.05) Do Not Reject. 0 1.50 Z Reject  = 0.05 1.96 p Value = 2 x 0.0668 Test Statistic 1.50 is in the Do Not Reject Region Reject

11. © 2001 Prentice-Hall, Inc. Chap 9-11 Two-tail Z Test for Mean ( Known) Assumptions Population is normally distributed If not normal, requires large samples Null hypothesis has an = sign is known Z Test Statistic

12. © 2001 Prentice-Hall, Inc. Chap 9-12 Summary Performed Z Test for the Mean ( Known) Discussed Critical Value Approach to Hypothesis Testing Discussed p –Value Approach to Hypothesis Testing