Question

A random sample of 850 students between the ages of 20 and 24 at a large midwestern university completed a survey including questions about their sleep quality, moods, academic performance, physical health, and psychoactive drug use. Sleep quality was measured using the Pittsburgh Sleep Quality Index (PSQI), with students scoring less than or equal to five on the index classified as optimal sleepers, those scoring a 6 or 7 classified as borderline, and those scoring over 7 classified as poor sleepers. The following table looks at the relationship between sleep quality classification and the use of over-the-counter (OTC) or prescription (Rx) stimulant medication more than once a month to help keep awake.

USE OF OTC/Rx MEDS TO WAKE > 1X/MONTH	SLEEP QUALITY ON PSQI INDEX
	OPTIMAL	BORDERLINE	POOR
Yes	34	50	81
No	265	177	243

Carry out a chi-square test.

Test H0:H0: there is no association between taking OTC medications to stay awake and sleep quality

versus Ha:Ha: there is an association between OTC medications to stay awake and sleep quality. Use α=0.01α=0.01.

χ2(±0.01)=χ2(±0.01)=

P(±0.0001)=P(±0.0001)=0.00005

There is evidence that there is an association between OTC medications to stay awake and sleep quality

There is no evidence that there is an association between OTC medications to stay awake and sleep quality

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Optimal	Borderline	poor	Total
	Yes	58.04	44.06	62.89	165
	No	240.96	182.94	261.11	685
	total	299	227	324	850
chi square    χ2	=(Oi-Ei)2/Ei	Optimal	Borderline	poor	Total
	Yes	9.958	0.799	5.212	15.9698
	No	2.399	0.193	1.256	3.8467
	total	12.3567	0.9920	6.4678	19.8166
test statistic X2=		19.82
p value =	0.0000	from excel: chidist(19.8166,2)

since p value <0.01

There is evidence that there is an association between OTC medications to stay awake and sleep quality