Course Notes - Department of Mathematics and Statistics

7 Hypothesis TestingFred’s Parking & Extracurricular activitiesFred’s wife Carol works downtown, and in an effort to discourage peoplefrom driving to work the council claim it takes on average 25 minutesto find a park. Fred does not think it takes so long to find a spot. Infact he has a sample of the last five times he drove to the downtownarea, and he calculated a sample mean of 15 minutes. Assume that thetime it takes to find a parking spot is normally distributed and that σ= 6 minutes. Is the council’s claim correct?When Fred was at university with Carol, they both were heavily involvedin extracurricular activities, Fred with his crochet and gardening,and Carol with her cage-fighting and yoga. They both got verygood grades at university, while their some of their friends did as littleextracurricular activity as possible, and only just passed their courses.Fred hypothesised then that extracurricular activity might increase peoplesgrades. He found some figures from the university of North Carolinathat looked at the pass rate of 124 students in a first year statisticspaper, which indicated that pass rate for students with no extracurricularactivites (40 students) was 55%, while it was 75% for students withbetween 2-12 hours of extracurricular activity (84 students). Is thereevidence to support Fred’s hypothesis?HYPOTHESES• In most scientific studies we set up hypotheses about treatmentsbefore collecting data.• These are the focus of the study.• A null hypothesis (H 0 ) is a claim about a treatment which isassumed to be true unless the data collected show substantialevidence against it.• The alternative hypothesis (H A ) is the one which is adopted ifthere is sufficient evidence against H 0 .119