Boles and Johnson (A-7) examined the beliefs held by adolescents regarding smoki
ID: 3208283 • Letter: B
Question
Boles and Johnson (A-7) examined the beliefs held by adolescents regarding smoking and weight. Respondents characterized their weight into three categories: underweight, overweight, or appropriate. Smoking status was categorized according to the answer to the question. "Do you currently smoke, meaning one or more cigarettes per day?" The following table shows the results of a telephone study of adolescents in the age group 12-17. Source: Sharon M. Boles and Patrick B. Johnson, "Gender, Weight Concerns, and Adolescent Smoking, " Journal of Addictive Diseases. 20 (2001), 5-14. Do the data provide sufficient evidence to suggest that weight perception and smoking status are related in adolescents? alpha = .05.Explanation / Answer
Solution:
Here, we have to check whether there is sufficient evidence to suggest that the weight perception and smoking status are related in adolescents or not. For checking this hypothesis or claim we have to use the Chi square test for the independence of two categorical variables. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The variables weight perception and smoking status are independent.
Alternative hypothesis: Ha: The variables weight perception and smoking status are not independent.
We are given a level of significance or alpha value as 5% or 0.05.
The test statistic formula is given as below:
Chi square = [(O – E)2/E]
The calculations and other values for this test are given as below:
Observed Frequencies
Smoking
Weight Perception
Yes
No
Total
Underweight
17
97
114
Overweight
25
142
167
Appropriate
96
816
912
Total
138
1055
1193
Expected Frequencies
Smoking
Weight Perception
Yes
No
Total
Underweight
13.19
100.81
114
Overweight
19.32
147.68
167
Appropriate
105.50
806.50
912
Total
138
1055
1193
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.991464547
Chi-Square Test Statistic
4.103341124
p-Value
0.128520023
Do not reject the null hypothesis
We conclude that the variables weight perception and smoking status are independent.
The data do not provide sufficient evidence to suggest that weight perception and smoking status are related in adolescents.
Observed Frequencies
Smoking
Weight Perception
Yes
No
Total
Underweight
17
97
114
Overweight
25
142
167
Appropriate
96
816
912
Total
138
1055
1193
Expected Frequencies
Smoking
Weight Perception
Yes
No
Total
Underweight
13.19
100.81
114
Overweight
19.32
147.68
167
Appropriate
105.50
806.50
912
Total
138
1055
1193
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.991464547
Chi-Square Test Statistic
4.103341124
p-Value
0.128520023
Do not reject the null hypothesis