SA3202, Solution for Tutorial 2 1. Day Mon Tue Wed Thu Fri Sat Sun Total # of Suicide 1001 1035 982 1033 905 737 894 6587 Expected 991.2 991.2 991.2 991.2 991.2 815.5 815.5 6587 H0: p1=p2=p3=p4=p5, p6=p7 (1 free parameter p1 while p6=(1-5*p1)/2 is not free ) T=26.4897, G=26.6882, df=7-1-1=5, 95% table=11.07. H0 is rejected. H0: p1=31/365, p2=28/365,…,p11=30/365, p12=31/365. (no free parameter) T=56.76, G=57.35, df=12-1-0=11. 95% table=19.675. Reject H0. 11/14/2018 SA3202, Solution for Tutorial 2

SA3202, Solution for Tutorial 2 3. For the Number of Boys Data, assume that the number of boys following a binomial distribution with probability ½: That is, H0: p0=1/16, p1=4/16, p2=6/16, p3=4/16,p4=1/16 (no parameter is free) T=14.26, df=5-1-0=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. (1 free parameter theta) The theta is estimated as .5158. T=.627. Df=5-1-1=3, 90%table=6.25, 95%table=7.81. Do not eject H0. More boys were born. 4. 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 Number of Boys Data, assume symmetry: H0: p0=p4,p1=p3 (2 free parameters p0, p1 while p2 =1-2(p0+p1) is not free) Oi 183 789 1250 875 246 Ei 214.5 832.0 1250.0 832.0 214.5 T=13. 6965, G=13.7320, df=5-1-2=2 , 95% table=5.991. Reject H0. The number of boys is not symmetric. 11/14/2018 SA3202, Solution for Tutorial 2