Homework SourseSmoking remains more common in much of Europe than in the Un
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 456 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.
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.
(b) We conjecture that men with a university education smoke less than the null hypothesis calls for. How does comparing the observed and expected counts in this row confirm this conjecture? Select all that apply
The nonsmoker count is higher than expected.
The heavy-smoker count is less than expected.
The heavy-smoker count is more than expected.
The nonsmoker count is lower than expected.
| Education | Smoking Status | ||||
| Nonsmoker | Former | Moderate | Heavy | ||
| Primary school | 58 | 53 | 39 | 38 | |
| Secondary school | 36 | 44 | 28 | 31 | |
| University | 52 | 26 | 35 | 16 |
Solution
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 456 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
39
38
Secondary school
36
44
28
31
University
52
26
35
16
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.
Nonsmoker
Former
Moderate
Heavy
Total
Primary school
60.19
50.71
42.05
35.04
188
Secondary school
44.50
37.49
31.09
25.91
139
University
41.30
34.80
28.86
24.05
129
Total
146
123
102
85
456
Calculations
fo-fe
-2.1930
2.2895
-3.0526
2.9561
-8.5044
6.5066
-3.0921
5.0899
10.6974
-8.7961
6.1447
-8.0461
(fo-fe)^2/fe
0.0799
0.1034
0.2216
0.2494
1.6251
1.1291
0.3075
0.9999
2.7706
2.2235
1.3085
2.6923
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
4
Degrees of Freedom
6
Results
Critical Value
12.592
Chi-Square Test Statistic
13.7108
p-Value
0.0330
Reject the null hypothesis
We conclude that the distribution of smoking is different for all three levels of education.
Nonsmoker
Former
Moderate
Heavy
Total
University
52
26
35
16
129
Expected
41.30
34.80
28.86
24.05
129
(b) We conjecture that men with a university education smoke less than the null hypothesis calls for. How does comparing the observed and expected counts in this row confirm this conjecture? Select all that apply
The nonsmoker count is higher than expected.
The heavy-smoker count is less than expected.
The heavy-smoker count is more than expected.
The nonsmoker count is lower than expected.
| Education | Smoking Status | ||||
| Nonsmoker | Former | Moderate | Heavy | ||
| Primary school | 58 | 53 | 39 | 38 | |
| Secondary school | 36 | 44 | 28 | 31 | |
| University | 52 | 26 | 35 | 16 |
