Solution for Tutorial 6 We have three types of sampling procedure: Simple Random Sampling, Stratified Sampling with column totals fixed, and with row totals fixed. For some data sets, we can only guess how the data was collected but sampling method does not affect the chi-square test of independence. It also does not affect inferences about the odds ratio. Data Set Type of Sampling Probability estimated correctly Vitamin C data clearly type 2 conditional on columns Seat Belt data seems to be type 1 joint, marginal or conditional Death Penalty data seems to be type 1 as the above (could be type 2) (conditional on columns) Univ. Admission data seems to be type 1 joint marginal, or conditional Smoking & Lung Cancer definitely type 2 conditional on columns Smoking habit most probably type 1 joint, margin, conditional (could be type 2) conditional on columns Income and Job Satisfaction probably type 1 joint, margin, conditional (could be type 3) conditional on rows Social Mobility data type 1 joint, marginal , and conditional Remark: For stratified sampling, we have information only about conditional probabilities. For example, for the Vitamin C data, we can not estimate the proportion of people who take vitamin C. 12/1/2018 SA3202, Solution 6

(a). Smoking and Lung Cancer We shall not give too many details, but the statistical values for your reference. (a). Smoking and Lung Cancer T=137.7, G=146.3, df=5, reject H0. There is a strong evidence for association. (b). Smoking Habit data T=37.6, G=38.4, df=2, reject H0. There is a strong evidence for association. (c ). Income and Job Satisfaction data T=11.99, G=12.04, df=9. Don’t reject H0. There is no strong evidence for association. (d). British Social Mobility data T=1176.5, G=792.2, df=16. Reject H0. There is a strong evidence for association. (e). Danish Social Mobility data T=754.1, G= 654.2, df=16. Reject H0. There is a strong evidence for association. So as expected, in both countries, there is strong evidence of association. Note that the association seems to be stronger in Britain than in Denmark for Britain is more class oriented?) 12/1/2018 SA3202, Solution 6

3. 12/1/2018 SA3202, Solution 6

(a) This is essentially verified in Problem 3. 12/1/2018 SA3202, Solution 6