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Statistics for Management Fundamentals of Hypothesis Testing
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
State its opposite, the Alternative Hypothesis ( H 1 : < 3)
Hypotheses are mutually exclusive & exhaustive
Sometimes it is easier to form the alternative hypothesis first.
Identify the Problem
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!
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
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
Reduce probability of one error and the other one goes up. & Have an Inverse Relationship
If not normal, only slightly skewed & a large sample taken
Parametric test procedure
t test statistic
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,
Do not reject at = .05 Z Test for Proportion: Solution H 0 : p .04 H 1 : p .04 Critical Values: 1.96 Test Statistic: Decision: Conclusion: We do not have sufficient evidence to reject the company’s claim of 4% response rate. Z p - p p (1 - p) n s = .04 -.05 .04 (1 - .04) 500 = -1.14 Z 0 Reject Reject .025 .025
Test Statistic: Decision: Conclusion: Reject at = 0.05 There is evidence of a difference in means. t 0 2.0154 -2.0154 .025 Reject H 0 Reject H 0 .025 t 3 27 2 53 1 510 21 25 2 03 . . . . Solution