Question

13. A random sample of 875 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)。 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 57 178 POOR 81 242 Yes No 276 Carry out a chi-square test. Test Ho : there is no association between taking OTC medications to stay awake and sleep quality versus H there is an association between OTC medications to stay awake and sleep quality. Use α 0.01 x" + (±0.0001) + = + P + (±0.000001) +-+ 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:

Expected	Ei=row total*column total/grand total	Optimal	Borderline	Poor	Total
	Yes	64.85	48.07	66.08	179
	No	252.15	186.93	256.92	696
	total	317	235	323	875
chi square    χ2	=(Oi-Ei)2/Ei	Optimal	Borderline	Poor	Total
	Yes	8.7708	1.6572	3.3705	13.798
	No	2.2557	0.4262	0.8668	3.549
	total	11.027	2.083	4.237	17.3473

X² =17.3473

p value =0.0002

there is evidence that there is an,,,,,,,,,,,