Question

Different lecture and tutorial rooms on campus are used by students from different Faculties. An important consideration when designing (and allocating) rooms on campus is the proportion of lefthanded seats available for left-handed students. To investigate this, UQ Property and Facilities Office sets up a booth at the Great Court to survey students on campus, asking each student whether they considered themselves left-handed or right-handed, and which Faculty they were in The results for the four most popular Faculties are shown below: Faculty Right-handed Left-handed Science 101 10 115 26 Health Science Engineering 121 83 16 Arts What overall proportion of students were left-handed in the survey? If there is in fact no difference in the proportion of left-handed students across all four Faculties, what counts would we expect to see in each cell of the table above? Write down the expected counts next to the observed counts in the table above Is there an association between handedness and which Faculty a student is enrolled in? Answer this question by carrying out an appropriate hypothesis test. You should clearly state the nl and alternative hypotheses, compute a p-value, and write a conclusion in a manner that can be understood by the UQ Property and Facilities Chief Operating Officer Identify one issue with the study design and one issue with the data collection iv. procedure v.Suggest one way to remedy one of the issues you identified in part (iv)

Answer 1

(i) overall proportion of left handed=57/477=0.1195

faculty	Right-handed	Left-handed	sum
Science	101	10	111
Health science	115	26	141
Engineering	121	5	126
Arts	83	16	99
sum=	420	57	477

(ii)

porportion of left handed	porportion of left handed	Expected frequency of left handed	Expected frequency of left handed
10/111=	0.0901	57/4=	14.25
26/141=	0.1844	57/4=	14.25
5/126=	0.0397	57/4=	14.25
16/99=	0.1616	57/4=	14.25

(iii) null hypothesis H0: There is no association between handedness and faculty

alternate hypothesis Ha: There is association between handedness and faculty

here we use chi-square test and

chi-square=sum((O-E)2/E)=15.85 with (r-1)(c-1)=(4-1)(2-1)=2 df

p-value=0.0004

since p-value is less than typical level of significance alpha=0.05, so we fail to accept H0 and conclude that there is association between handedness and faculty.

	Observed(O)	Expected(E)	E	(O-E)	(O-E)2/E
	101	111*420/477	97.74	3.26	0.11
	115	141*420/477	124.15	-9.15	0.67
	121	126*420/477	110.94	10.06	0.91
	83	99*420/477	87.17	-4.17	0.20
	10	111*57/477	13.26	-3.26	0.80
	26	141*57/477	16.85	9.15	4.97
	5	126*57/477	15.06	-10.06	6.72
	16	99*57/477	11.83	4.17	1.47
sum=	477	0	477	1.6E-14	15.85