Hypothesis Testing Approach 1 - Fixed probability of Type I error. 1.State the null and alternative hypotheses. 2.Choose a fixed significance level α. 3.Specify the appropriate test statistic and establish the critical region based on α. Draw a graphic representation. 4.Compute the value of the test statistic based on the sample data. 5.Make a decision to reject or fail to reject H 0, based on the location of the test statistic. 6.Draw an engineering or scientific conclusion.

Hypothesis Testing Approach 2 - Significance testing (P-value approach) 1.State the null and alternative hypotheses. 2.Choose an appropriate test statistic. 3.Compute value of test statistic and determine P-value. 4.Draw conclusion based on P- value. P = 0P =

Single Sample Test of the Mean A sample of 20 cars driven under varying highway conditions achieved fuel efficiencies as follows: Sample mean x = mpg Sample std dev s = mpg Test the hypothesis that the population mean equals 35.0 mpg vs. μ < 35. H 0 : ________n = ________ H 1 : ________ σ unknown use ___ distribution.c

Example (cont.) Approach 2: = _________________ Using Excel’s tdist function, P(x ≤ ) = _____________ Conclusion: __________________________________

Example (concl.) Approach 1: t 0.05,19 = _____________ Since H 1 specifies “< μ,” t crit = ___________ t calc = _________ Conclusion: _________________________________

Hypothesis Testing Tells Us … Strong conclusion: –If our calculated t-value is “outside” t α, ν (approach 1) or we have a small p-value (approach 2), then we reject H 0 : μ = μ 0 in favor of the alternate hypothesis. Weak conclusion: –If our calculated t-value is “inside” t α, ν (approach 1) or we have a “large” p-value (approach 2), then we cannot reject H 0 : μ = μ 0. In other words: –Failure to reject H 0 does not imply that μ is equal to the stated value, only that we do not have sufficient evidence to favor H 1.

Your turn … A sample of 20 cars driven under varying highway conditions achieved fuel efficiencies as follows: Sample mean x = mpg Sample std dev s = mpg Test the hypothesis that the population mean equals 35.0 mpg vs. μ ≠ 35 at an α level of Draw the picture.

Homework for Wednesday, Nov. 3 pp : 5, 12, 15 pp : 3, 4, 6, 7, 8