BIOL 570 1st Edition Lecture 8 Outline of Last Lecture I. probability reviewII. distributionsIII. probability trees.Outline of Current Lecture I. 7 steps of hypothesis tests a. hypothesesb. test statisticc. null distributiond. P-valuee. alphaf. reporting resultsCurrent LectureInferenceEstimation (confidence interval)Proportion Hypothesis Hypothesis testing (7 steps Bb handout) Example 1Step 1: Does wearing a red shirt help win a wrestling contest?Step 2:HO: Red and blue shirted are equally likely to win. Proportion of red shirted wins in a population of contests = 0.5. P=.5HA: opposite of HO P≠ .5- null hypothesis, HO: no effect, no differenceo population parameter, very specific- alternative hypothesis, Ha: effect, difference o population parameter, generalThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.o 2 sidedStep 3: 20 contestsStep 4: 16/20 (winner wore red)Step 5: a) Test statistic = 161. Calculated from data2. Allows us to see how compatible the data are with the HO (null)b) HO is trueP-value= P (16) + P (17) + … P (20) + P (4) + P (3) + … P (0) = .012 (very unlikely, not impossible)Step 6: P = .012 α = .05.012 ≤ .05 reject- Go with alternative P ≠ .5Step 7: In a study of 20 matches at the 2004 Olympics 12 (80%) of the winners wore red shirts, this result is significantly greater than expected by chance (P = .012). Example 2Step 1: Do dogs resemble their owners?Step 2:HO: In a population of possible dog, owner, other dog combinations the proportion of correct matches = .5 P=.5100911Population:Possible matchesn =20HA: P≠ .5Step 3: 41 sets (random sample)Step 4: 23 correct matches (descriptive statistic = results)Step 5: a) Test statistic = 23 (test statistic = results)1. Calculated from data2. Allows us to see how compatible the data are with the HO (null)b) P-value = area that’s shaded in the null distributionc) P- value = shaded areaStep 6: do NOT rejectP = .53 α = .05P-value > α.53 > .05 Step 7: We found no evidence (P = 0.53) that dogs resemble their owners; correct matches were made only 56% of the time (23 of 41 total