Analysis of Scientific Data -Summer Semester, 2021 Week 7 Tutorial Questions Part A - Chi-square test Question 1 In semester 2 2020, 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? 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?
Question 2 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 2020 454 185 139 Is there any evidence of a change in living situations between 2018 and 2020?
Part B - Logistic regression A researcher investigated the relationship of being obese and the weight using the following logistic regression model. ln d = Bo + B1X 1 - p Where p = probability of being obese and X = Weight (in kgs) The results of the maximum likelihood method in R is given below. Call: glm(formula = obese ~ Weight, family = "binomial", data = obesity) Deviance Residuals: Min 1Q Median -1.9206 -0.8743 -0.4767 3Q 0.8854 Max 2.3033 Coefficients: Estimate Std. Error z value Pr (>|z|) (Intercept) -6. 24779 Weight 0.08337 2.18610 -2. 858 0.00426 ** 0.02956 2.820 0.00480 ** a) Write down the estimated logistic regression equation. b) What is the estimated probability of being obese for an individual whose weight is 90kgs?