Health Promotion It is fairly well known that perception of weight by adolescent
ID: 3128622 • Letter: H
Question
Health Promotion
It is fairly well known that perception of weight by adolescents does not always agree with actual weight. What is less clear is whether perception of weight differs by gender. For this purpose, a study was performed among students in a local high school, where students provided their actual height and weight by self-report. The following data were obtained from 286 students (143 boys and 143 girls). (The data for this problem were provided by Laura Rosner.) The students were classified as underweight if their body-mass index (BMI) (kg/m2) was less than 18.0 kg/m2, as normal if their BMI was 18.0 and < 25.0, and overweight if their BMI was 25.0. Based on these criteria, 17 of the girls were underweight, 113 were of normal weight, and 13 were overweight. For the boys, 7 were underweight, 115 were of normal weight, and 21 were overweight.
What test procedure can be used to assess whether the weight status of boys significantly differs from girls? Perform the test procedure and provide a two-tailed p-value.
Explanation / Answer
It is fairly well known that perception of weight by adolescents does not always agree with actual weight. What is less clear is whether perception of weight differs by gender. For this purpose, a study was performed among students in a local high school, where students provided their actual height and weight by self-report. The following data were obtained from 286 students (143 boys and 143 girls). (The data for this problem were provided by Laura Rosner.) The students were classified as underweight if their body-mass index (BMI) (kg/m2) was less than 18.0 kg/m2, as normal if their BMI was 18.0 and < 25.0, and overweight if their BMI was 25.0. Based on these criteria, 17 of the girls were underweight, 113 were of normal weight, and 13 were overweight. For the boys, 7 were underweight, 115 were of normal weight, and 21 were overweight.
What test procedure can be used to assess whether the weight status of boys significantly differs from girls?
Chi square test can be used.
Null hypothesis: the weight status of boys not differs from girls
Alternate hypothesis: the weight status of boys significantly differs from girls
Perform the test procedure and provide a two-tailed p-value.
test statistic = 6.067
P=0.0482
Null hypothesis is rejected.
We conclude that the weight status of boys significantly differs from girls.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
underweight
normal
overweight
Total
fo-fe
Girls
17
113
13
143
5
-1
-4
Boys
7
115
21
143
-5
1
4
Total
24
228
34
286
Expected Frequencies
Column variable
underweight
normal
overweight
Total
(fo-fe)^2/fe
Girls
12
114
17
143
2.0833
0.0088
0.9412
Boys
12
114
17
143
2.0833
0.0088
0.9412
Total
24
228
34
286
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.9915
Chi-Square Test Statistic
6.0666
p-Value
0.0482
Reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
underweight
normal
overweight
Total
fo-fe
Girls
17
113
13
143
5
-1
-4
Boys
7
115
21
143
-5
1
4
Total
24
228
34
286
Expected Frequencies
Column variable
underweight
normal
overweight
Total
(fo-fe)^2/fe
Girls
12
114
17
143
2.0833
0.0088
0.9412
Boys
12
114
17
143
2.0833
0.0088
0.9412
Total
24
228
34
286
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.9915
Chi-Square Test Statistic
6.0666
p-Value
0.0482
Reject the null hypothesis
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