Question

Smoking remains more common in much of Europe than in the United States. 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? Here is a two-way table of the level of education and smoking status (nonsmoker, former smoker, moderate smoker, heavy smoker) of a sample of 467 French men aged 20 to 60 years. The subjects are a random sample of men who visited a health center for a routine checkup. We are willing to consider them an SRS of men from their region of France.

Education		Smoking Status
		Nonsmoker	Former	Moderate	Heavy
Primary school		58	53	41	38
Secondary school		39	42	28	32
University		53	27	38	18

The null hypothesis states that there is no relationship between these variables. That is, the distribution of smoking is the same for all three levels of education.

(a) Find the expected counts for each smoking status among men with a university education. This is one row of the two-way table of expected counts. Find the row total and verify that it agrees with the row total for the observed counts.

Use two decimals for the expected counts and a whole number for the total.

Education		Smoking Status				TOTAL
		Nonsmoker	Former	Moderate	Heavy
University
Expected

Answer 1

Part a

We are given observed frequencies as below:

Observed Frequencies
	Smoking Status
Education	Non-smoker	Former	Moderate	Heavy	Total
Primary	58	53	41	38	190
Secondary	39	42	28	32	141
University	53	27	38	18	136
Total	150	122	107	88	467

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

For the first cell, expected frequency is given as below:

E = 150*190/467 = 61.03

In the same way, all expected frequencies are summarised in the following table:

Expected Frequencies
	Smoking Status
Education	Non-smoker	Former	Moderate	Heavy	Total
Primary	61.03	49.64	43.53	35.80	190
Secondary	45.29	36.84	32.31	26.57	141
University	43.68	35.53	31.16	25.63	136
Total	150	122	107	88	467