Statistical Inference for Managers

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Presentation transcript:

Statistical Inference for Managers Hypothesis Testing Statistical Inference for Managers

Hypothesis Testing Hypothesis is a statement about parameter of a population which may or may not be true. Or Process by which we conclude that given statement is true or not is called hypothesis testing. The base hypothesis with which we are testing is called null hypothesis (Ho). The opposite (negation) of null hypothesis is called alternative hypothesis (H1).

Type-1 error: Rejecting a true null hypothesis is called type 1 error Type-1 error: Rejecting a true null hypothesis is called type 1 error. Type-II error: Accepting a false null hypothesis is called type II error. Level of significance: Is the probability of type 1 error. That is the probability of considering H0 false when it is actually true (alpha). Power of Test: Is the probability of not doing type II error (1-β) Critical region: Is set of values in which if our calculated value lies the we reject Ho.

Steps for Hypothesis Testing Write Ho Write H1 Decide level of significance Write critical region Do calculations called test statistics Conclusion

Cases Case-1: Test for population mean when population standard deviation is known: Case-2: Test for population mean when population standard deviation is unknown and n>30:

Cases Case-3: Test for population mean when population standard deviation is unknown and n<30. Case-4: Test for difference of two population means when σ1 & σ2 are known.

cases Case-5: Test for difference of two population means when σ1 & σ2 are unknown and n1>30, n2>30 Case-6: Test for difference of two population means when σ1 & σ2 are unknown and n1<30, n2<30

cases Case-7: Test for population proportion: Case-8: Test for difference of two population proportions:

Example: The production Manager of Northern Windows has asked you to evaluate a proposed new procedure for producing its Regal Line of double-hung windows. The present process has a mean production of 80 units per hour with a population standard deviation of 8. The manager indicates that she does not want to change to a new procedure unless there is a strong evidence that the mean production level is higher with the new process. N=25 Xbar=83