Hypothesis Testing Approach 1 Fixed probability of Type

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

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 Pvalue. P=0 0. 25 0. 75 P=1

Single Sample Test of the Mean A sample of 20 cars driven under varying highway conditions achieved fuel efficiencies as follows: Sample mean Sample std dev x = 34. 271 mpg s = 2. 915 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 ≤ -1. 118) = _______ Conclusion: _________________

Example (concl. ) Approach 1: t 0. 05, 19 = _______ Since H 1 specifies “< μ, ” tcrit = ______ tcalc = _____ Conclusion: _________________

Hypothesis Testing Tells Us … • Strong conclusion: – If our calculated t-value is “outside” tα, 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” tα, 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 Sample std dev x = 34. 271 mpg s = 2. 915 mpg Test the hypothesis that the population mean equals 35. 0 mpg vs. μ ≠ 35 at an α level of 0. 05. Draw the picture.

Homework for Wednesday, Nov. 3 • pp. 298 -299: 5, 12, 15 • pp. 319 -323: 3, 4, 6, 7, 8