SA3202, Solution for Tutorial 1 Digit 1 2 3 4 5 6 7 8 9 0 Total Observed Freq. 7 11 7 12 11 6 15 9 13 9 100 Expected Freq. 10 10 10 10 10 10 10 10 10 10 100 (no free parameter) T=7.6, G=7.8825, df=10-1-0=9, 95% table=16.92, 90% table=14.68. Don’t reject H0. The digits follow the equi-probability model. Day Mon Tue Wed Thu Fri Sat Sun Total # of Suicide 1001 1035 982 1033 905 737 894 6587 Expected 941 941 941 941 941 941 941 6587 (Expected) 1013 1013 1013 1013 899 737 899 6587 T=71.95, G=78.38, df=7-1-0=6, 95% table=12.59, 90%table=10.6446 Reject H0. That is, the data do not follow the equi-probability model. H0: p1=p2=p3=p4, p5=p7 (2 free parameters: p1, p5 while p6=1-(4p1+2p5) is not free) T=2.031, G=2.039, df=7-1-2=4, 95% table=9.488, 90% table=7.779. Do not reject H0. 11/14/2018 SA3202, Solution for Tutorial 1

SA3202, Solution for Tutorial 1 3. T=87.43, df= 12-1=11, 95%table=19.675, 90%table=17.275. Reject H0. Assume a new model that the probability for a month is proportional to the days of the month: H0: p1=31/365, p2=28/365,…,p11=30/365,p12=31/365. (no free parameter) T=56.76, G=57.35, df=12-1=11. 95% table=19.675. Reject H0. It is clear that the equi-probability model doesn’t fit the data sets. For the Number of Boys Data, assume that the number of boys following a binomial distribution with probability ½: H0: p0=1/16, p1=4/16, p2=6/16, p3=4/16,p4=1/16 (no free parameter) T=14.26, df=5-1=4, 95% table=9.488, 90% table=7.779. Reject H0. Assume that the number of boys following a binomial distribution with unknown success probability theta. The theta is estimated as .5158. (1 free parameter) T=.627. Df=5-1-1=3, 90%table=6.25, 95%table=7.81. Do not eject H0. More boys were born. For the Political View Data, assume that the political views are symmetric: H0: p1=p7, p2=p6, p3=p5. ( 3 free parameters p1, p2,p3 while p4=1-2(p1+p2+p3) is not free) T=7.078, df=7-1-3=3, 90%table=6.25, 95%table=7.81. Do not eject H0 when alpha=5%. For the World Cup Data, we may assume a Poisson distribution for the # of Goals. Shall discuss more in future lectures and tutorials. 11/14/2018 SA3202, Solution for Tutorial 1