1. SA3202, Solution for Tutorial 1
Digit Total
Observed Freq
Expected Freq
(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
Expected
(Expected)
T=71.95, G=78.38, df=7-1-0=6, 95% table=12.59, 90%table=
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= Do not reject H0.
11/14/2018
SA3202, Solution for Tutorial 1

2. SA3202, Solution for Tutorial 1
3. T=87.43, df= 12-1=11, 95%table=19.675, 90%table= 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= % table= 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= Reject H0.
Assume that the number of boys following a binomial distribution with unknown success probability theta.
The theta is estimated as (1 free parameter)
T= 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