2. Statistics for Decision Making Hypothesis Testing QM 2113 -- Fall 2003 Instructor: John Seydel, Ph.D.

3. Student Objectives Compare and contrast the two types of statistical inference Define hypothesis testing and summarize the basic process Discuss errors that can be made in statistical inferences Use sample data to test claims about population parameters

4. Sampling Distributions (Review) Data TypeParameterEstimatorStdError Quantitative  Qualitative  Note: these estimators are approximately normally distributed; i.e., their sampling distributions are approximately normal

5. Review of Statistical Inference Recall: there are only 2 types of inference Estimation (confidence intervals) Hypothesis testing Confidence intervals Parameter ≈ Point Estimate ± Margin of Error Margin of error is based upon confidence level  Margin of error = z-score ∙ standard error  Example, for confidence of 95%: 2 ∙ (s/√n) 2 ∙ (√[(p)(1 - p)/n]) Hypothesis testing (see overview)overview

6. Hypothesis Testing Examples Quantitative data (from text): 3, 4, 5 Qualitative data We haven’t discussed this, but it works the same! Text: 28, 29, 30 Now, about p-values Just another way to express the DR Note: three types of DRDR

7. Summary of Objectives Compare and contrast the two types of statistical inference Define hypothesis testing and summarize the basic process Discuss errors that can be made in statistical inferences Use sample data to test claims about population parameters

8. Appendix

9. Sampling Population Sample Parameter Statistic

10. The Other Kind of Inference: Hypothesis Testing Recall that there are only 2 types of inference Estimation (confidence intervals) Hypothesis testing Starts with a hypothesis (i.e., claim, assumption, standard, etc.) about a population parameter ( , , ,  , distribution,... ) Sample results are compared with the hypothesis Based upon how likely the observed results are, given the hypothesis, a conclusion is made

11. Hypothesis Testing Start by defining hypotheses Null (H 0 ):  What we’ll believe until proven otherwise  We state this first if we’re seeing if something’s changed Alternate (H A ):  Opposite of H 0  If we’re trying to prove something, we state it as H A and start with this, not the null Then state willingness to make wrong conclusion (  ) Draw a sketch of the sampling distribution Determine the decision rule (DR) Gather data and compare results to DR

12. Stating the Decision Rule Recall that no analysis should take place before DR is in place! Can state any of three ways Critical value of observed statistic (x-bar or p) Critical value of test statistic (z) Critical value of likelihood of observed result (p-value) Generally, test statistics are used when results are generated manually and p-values are used when results are determined via computer Always indicate on sketch of distribution

13. Errors in Hypothesis Testing Type I: rejecting a true H 0 Type II: accepting a false H 0 Probabilities  = P(Type I)  = P(Type II) Power = P(Rejecting false H 0 ) = P(No error) Controlling risks Decision rule controls  Sample size controls  Worst error: Type III (solving the wrong problem)! Hence, be sure H 0 and H A are correct