A random sample of 880 students between the ages of 20 and 24 at a large midwest

Question

A random sample of 880 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.

Carry out a chi-square test. Test H0: there is no association between taking OTC medications to stay awake and sleep quality versus Ha: there is an association between OTC medications to stay awake and sleep quality. Use =0.01.

2(±0.01)=

P(±0.0001)=

Select ONE.

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

USE OF OTC/Rx MEDS
TO WAKE > 1X/MONTH SLEEP QUALITY ON PSQI INDEX OPTIMAL BORDERLINE POOR Yes 34 48 89 No 268 186 255

Explanation / Answer

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

H1: there is an association between OTC medications to stay awake and sleep quality

The observed frequencies are

The Expected frequencies are

The Chi-Square test statistic is calculated as

Degrees of freedom: (2-1)(3-1) = 2 df

Test Statistic, X^2: 73.0530
Critical X^2:        9.210334
P-Value:             0.0000

Here Test Statistic X^2 > Critical X^2 and P value < alpha (0.05) so we reject H0.

Thus, we conclude that there is evidence that there is an association between OTC medications to stay awake and sleep quality

Correct Answer; Option (B)

Optimal Borderline Poor Total Yes 212 315 245 772 No 87 64 196 347 Total 299 379 441 1119

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