STT 231 recitation 4

SS24 STT 231: Statistics for Scientists Week 4 Recitation Activity: Investigating associations & independence Your name: _______________________________________ Your NetID : _____________________________________ 1. Suppose that you ask dog and cat owners whether their pet has been to a veterinarian in the past twelve months. You organize your results in a 2x2 table like the one below. For each of the following exercises, create your own example of counts that satisfy the indicated property, assuming that an individual owns either a cat or a dog, but not both. Do this by filling in the appropriate cells of the table with counts. Also report the values for all relevant proportions and relative risks. Let ^ π i = the proportion of owners for the 𝑖 𝑡ℎ animal who indicated that ‘yes,’ they had taken their pet to the vet in the past 12 months. a. The difference in conditional proportions (cats – dogs) who answer ‘yes’ is exactly 0.2 and the ratio of proportions is less than 1.4. Dog owner Cat owner Yes 60 40 No 40 10 Total 100 50 𝜋̂ 𝑐𝑎𝑡 = __40/50=0.8_____ R.R. = ^ π cat ^ π dog = ___1.333____ 𝜋̂ 𝑑𝑜𝑔 = ___60/100=0.6________ b. The difference in conditional proportions (cats – dogs) who answer ‘yes’ is more than 0.1 and the ratio of proportions (i.e., the relative risk) who answer ‘yes’ is exactly 2.0. Dog owner Cat owner Yes 30 30 No 70 20 Total 100 50 𝜋̂ 𝑐𝑎𝑡 = ____30/50=0.6__ R.R. = ^ π cat ^ π dog = ¿ ___2_____ 𝜋̂ 𝑑𝑜𝑔 = __30/100=0.3______ c. The difference in conditional proportions (cats – dogs) who answer yes is greater than 0.2 and the relative risk is greater than 2.0. Dog owner Cat owner Yes 30 45 No 70 5 Total 100 50 𝜋̂ 𝑐𝑎𝑡 = ___45/50=0.9_____ R.R. = ^ π cat ^ π dog = __3____ 𝜋̂ 𝑑𝑜𝑔 = __30/100=0.3_____ d. The difference in conditional proportions (cats – dogs) who answer yes is greater than 0.2 and the relative risk is less than 2.0. Dog owner Cat owner Yes 40 20 No 60 30 Total 100 50 Dog owner Cat owner Yes ?? ?? No ?? ?? Total 100 50