Analysis of Scientific Data - Semester 2, 2020 Week 12 Tutorial Question 1 In Lecture 3.1 this semester, students were asked in a Zoom poll to "toss a coin twice and indicate your outcome". The combined counts from the two streams are shown in the following table: HH HT TH TT 63 80 64 42 a) Supposing these were independent tosses of fair coins, how many counts would you expect in each of these four groups? (63+80+64+42)/4 = 62.25 b) Calculate the statistic to compare the observed counts to the expected count. Is there any evidence that this process did not work as intended? 1-pchisq(11.71,df=3) = 0.00844557 (1 - because we want the right side of distribution) Strong evidence that the process did not work as intended Question 2 One of the survey questions this semester was "How many minutes have you spent exercising in the last 48 hours?" For a random sample of 30 students, their mean response was 57.5 minutes with a standard deviation of 54.03 minutes. a) Is there evidence that statistics students are getting at least 20 minutes of exercise per day? pt(-1.774,df=29) = 0.04328234 b) Do you have any concerns about your analysis? Very large standard deviation and variation
Question 3 The following table shows counts of students in the 2018 and 2020 surveys who lived at home or in a shared flat/house: Year Home Shared Flat/House 2018 391 185 2020 454 139 Is there any evidence of a change in living situations between 2018 and 2020? With df = (2-1)(2-1) = 1, 1-pchisq(11.02,df=1) = 0.0009013407 You may find the following useful in answering the questions on this sheet. Very strong evidence " 0"= $ expected (observed - expected) expected = overall4total (row4total) x (column4total) df=(#rows - 1) × (#columns - 1) > pt(1.774,df=29) [1] 0.9567177 > 2*pt(-1.774,df=29) [1] 0.0009013407 [1] 0.08656468 > pt(-1.774,df=29) [1] 0.04328234 > pchisq(11.71,df=3) [1] 0.9915544 > 1-pchisq(11.71,df=3) [1] 0.00844557 > 1-pchisq(11.71,df=248) [1] 1 > 1-pchisq(11.02,df=3) [1] 0.01161822 > 1-pchisq(11.02,df=1) > pchisq(11.02,df=1) [1] 0.9990987 > 1-pchisq(0.434,df=1) [1] 0.5100327