Question

It is a general belief that in the United States there is a strong relationship between education and smoking: well-educated people are less likely to smoke. Does a similar relationship hold in France? To find out, researchers recorded the level of education and status of a random sample 459 French men aged 20 to 60. The two-way table below displays the data.

Smoking Status
Education	Nonsmoker	Former	Moderate	Heavy
Primary school Secondary school University	56 37 53	54 43 28	41 27 36	36 32 16

a. State the test you plan to use and determine whether the conditions for test are satisfied.

b. State the hypotheses for this test.

c. At alpha = 0.05, determine whether there is a significant relationship between smoking status and educational level.

Answer 1

a)here as we are testing if smoking status and educational level have any relatioship based on given contingency table

therefore we will apply chi square test of independence.

b)

null hypothesis:Ho: smoking status and educational level are independent

alternate hypothesis: Ha:smoking status and educational level are dependent

c)

degree of freedom =(row-1)*(column-1)=(3-1)*(4-1)=6

for 6 df and 0.05 level of significance rejection region   >=12.592

applying chi square test:

Observed	OBS	nonsmoker	former	mderate	heavy	Total
	primary	56	54	41	36	187
	secondary	37	43	27	32	139
	university	53	28	36	16	133
	Total	146	125	104	84	459
Expected	Ei=?row*?column/?total	nonsmoker	former	mderate	heavy	Total
	primary	59.481	50.926	42.370	34.222	187
	secondary	44.214	37.854	31.495	25.438	139
	university	42.305	36.220	30.135	24.340	133
	Total	146	125	104	84	459
chi square	=(Oi-Ei)2/Ei	nonsmoker	former	mderate	heavy	Total
	primary	0.20	0.19	0.04	0.09	0.53
	secondary	1.18	0.700	0.641	1.693	4.21
	university	2.70	1.866	1.141	2.858	8.57
	Total	4.08	2.75	1.83	4.64	13.305

here as test statsitic 13.305 lies in rejectioin region we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that tehre is a significant relationship between smoking status and educational level.