Question

 

The table below shows the number of graveyard shift, swing shift, and day shift workers (variable called JOB SHIFT) by "coffee drinking" and "non-coffee drinking" (variable called AWAKE). Test the null hypothesis that the two variables are unrelated by doing the following:

(Answer: Chi-square = 10.08)

1. State the null and research hypotheses.
2. Report the degrees of freedom.
3. Report the critical value (use alpha = .05)
4. Calculate the test statistic
5. In two or three sentences, briefly explain the results

(this includes your decision concerning the null hypothesis).

JOB SHIFT

Graveyard     Swing       Day

AWAKE

Coffee drinkers                                          45              35            25

Non-coffee drinkers                                   24              26            40

Answer 1

H0: Two variables are unrelated

H1: Two variables are related

let the los be alpha = 5%

The observed frequencies are

	Graveyard	Swing	Day	Total
Coffee drinkers	45	35	25	105
Non Coffee drinker	24	26	40	90
Total	69	61	65	195

The expected frequencies are

	Graveyard	Swing	Day	Total
Coffee drinkers	37.154	32.846	35	105
Non Coffee drinker	31.846	28.154	30	90
Total	69	61	65	195

The chi-square contribution values are

Oi	Ei	(Oi-Ei)	(Oi-Ei)^2 /Ei
45	37.154	7.846	1.6569
35	32.846	2.154	0.1413
25	35	-10	2.8571
24	31.846	-7.846	1.933
26	28.154	-2.154	0.1648
40	30	10	3.3333
	Total:		10.0864

Degrees of freedom: 2

Test Statistic, X^2: 10.0865

Critical X^2: 5.991471

Since Chi-square value > Chi-square critical value so we reject H0

Thus we conclude that  two variables are related