Chapter 11, Problem T11.13SPT

To determine

To perform hypothesis testing.

Answer to Problem T11.13SPT

There is convincing evidence that there is association between education and smoking status.

Explanation of Solution

Given:

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

The null and alternative hypotheses:

  $H_0$ : There is no association between education and smoking status.

  $H_a$ : There isassociation between education and smoking status.

Using excel,

		Primary school	Secondary	University	Total
Nonsmoker	Observed	56	37	53	146
	Expected	59.48	44.21	42.31	146.00
	(O - E)² / E	0.20	1.18	2.70	4.08
Former	Observed	54	43	28	125
	Expected	50.93	37.85	36.22	125.00
	(O - E)² / E	0.19	0.70	1.87	2.75
Moderate	Observed	41	27	36	104
	Expected	42.37	31.49	30.14	104.00
	(O - E)² / E	0.04	0.64	1.14	1.83
Heavy	Observed	36	32	16	84
	Expected	34.22	25.44	24.34	84.00
	(O - E)² / E	0.09	1.69	2.86	4.64
Total	Observed	187	139	133	459
	Expected	187.00	139.00	133.00	459.00
	(O - E)² / E	0.53	4.21	8.57	13.30
		13.30	chi-square
		6	df
		.0384	p-value

Chi-square test statistic = 13.30. The degrees of freedom = 6 and p-value = 0.0384

Decision: P-value < 0.05, reject H0.

Conclusion: There is convincing evidence that there is association between education and smoking status.