Question

4.

A random sample of 859 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	31	47	86
No	265	188	242

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)=

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

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

Answer 1

Ans:

	Observed(fo)
	optimal	borderline	poor	Total
Yes	31	47	86	164
No	265	188	242	695
Total	296	235	328	859
	Expected(fe)
	optimal	borderline	poor	Total
Yes	56.51	44.87	62.62	164
No	239.49	190.13	265.38	695
Total	296	235	328	859
	Chi square=(fo-fe)^2/fe
	optimal	borderline	poor	Total
Yes	11.52	0.10	8.73	20.35
No	2.72	0.02	2.06	4.80
Total	14.24	0.13	10.79	25.15

Test statistic:

Chi square=25.15

df=(2-1)*(3-1)=2

p-value=CHIDIST(25.15,2)=0.0000

As,p-value<0.01,we reject the null hypothesis.

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