1. Statistics for Management Fundamentals of Hypothesis Testing
2. Lesson Topics 1. What is a Hypothesis? Hypothesis Testing Methodology Hypothesis Testing Process Level of Significance, a Errors in Making Decisions 2. Hypothesis Testing: Steps Z Test for the Mean (s Known) Connection to Confidence Interval Estimation Hypothesis Testing Methodology
3.
4.
5.
6.
7. Population Assume the population mean age is 50. (Null Hypothesis) REJECT The Sample Mean Is 20 Sample Null Hypothesis Hypothesis Testing Process No, not likely!
8. Sample Mean = 50 Sampling Distribution It is unlikely that we would get a sample mean of this value ... ... if in fact this were the population mean. ... Therefore, we reject the null hypothesis that = 50. 20 H 0 Reason for Rejecting H 0
9.
10. Level of Significance, and the Rejection Region H 0 : 3 H 1 : < 3 0 0 0 H 0 : 3 H 1 : > 3 H 0 : 3 H 1 : 3 /2 Critical Value(s) Rejection Regions
11.
12. H 0 : Innocent Jury Trial Hypothesis Test Actual Situation Actual Situation Verdict Innocent Guilty Decision H 0 True H 0 False Innocent Correct Error Do Not Reject H 0 1 - Type II Error ( ) Guilty Error Correct Reject H 0 Type I Error ( ) Power (1 - ) Result Possibilities
13. Reduce probability of one error and the other one goes up. & Have an Inverse Relationship
14.
15.
16.
17.
18.
19. Z 0 Reject H 0 Z 0 Reject H 0 H 0 : H 1 : < 0 H 0 : 0 H 1 : > 0 Must Be Significantly Below = 0 Small values don’t contradict H 0 Don’t Reject H 0 ! Rejection Region
20.
21. Z .04 .06 1.6 . 5495 . 5505 .5515 1.7 .5591 .5599 .5608 1.8 .5671 .5678 .5686 .5738 .5750 Z 0 Z = 1 1.645 .50 -. 05 .45 . 05 1.9 .5744 Standardized Normal Probability Table (Portion) What Is Z Given = 0.05 ? = .05 Finding Critical Values: One Tail Critical Value = 1.645
22.
23.
24.
25.
26.
27. Example: One Tail t-Test Does an average box of cereal contain more than 368 grams of cereal? A random sample of 36 boxes showed X = 372.5 , and S= 15 . Test at the 0.01 level. 368 gm. H 0 : 368 H 1 : 368 is not given,
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40. t X X S n n S n S n S n n P P 1 2 1 2 2 1 2 2 1 1 2 2 2 2 1 2 2 2 3 27 2 53 0 1 510 21 25 2 03 1 1 1 1 21 1 1 30 25 1 1 16 21 1 25 1 1 510 . . . . . . . Calculating the Test Statistic: ( ( ( ( ( ( ( ( ( ( ( ) ) ) ) ) ) ) ) ) ) )