STATISTICS 1403 PROBABILITY AND STATISTICS FOR BIOSCIENCES PROBLEM SET: PAIRED TEST AND POWER Abstract. Solve these problems, and prepare a clean, annotated copy of them. 1. A Paired t Test Researchers studied the efficacy of saliva continine as an indicator for exposure to tobacco smoke. Seven subjects–none heavy smokers–abstained from smoking for a week, and then smoked a single cigarette. Continine levels in their saliva were measured 12 and 24 hours after the exposure: continine levels, nmol/l subject after 12 hours after 24 hours 1 72 24 2 58 27 3 67 49 4 93 59 5 33 0 6 18 11 7 147 43 Test the research hypothesis that the continine level decreases over time at the α = 0.01 level. Useful Formulas. di = y1,i − y2,i t= p d¯ s2d /n 2. Power Smoking It turns out this experiment was only a pilot study whose main purpose was to estimate the mean difference and the variance of differences. Use the variance information calculated from the previous problem to estimate the number of subjects needed to conduct the test and detect a mean difference of µd = 30 with Type I error α = 0.01 and power 1 − β = 0.95. Use z-value critical values (rather than t values) to simplify your calculations. Useful Formula. σ 2 (z1−α − zβ )2 n= (µa − µ0 )2 1