In: Statistics and Probability
A team of researchers wanted to assess the effectiveness of the 4 components of a weight loss program by comparing the distribution of weight status across 4 different treatment groups. The data is summarized in the table below:
|
Weight Status |
|||
|
Intervention Component |
Normal Weight |
Overweight |
Obese |
|
Control Group (n=100) |
50 |
35 |
15 |
|
Calorie Counting (n=100) |
70 |
20 |
10 |
|
Physical Activity (n=100) |
73 |
15 |
12 |
|
Combination (n=100) |
80 |
15 |
5 |
Is there a difference in weight status by intervention component? (Hint: Are intervention component and weight status independent?) Run the appropriate test at a 5% level of significance.
|
Weight Status |
||||
|
Intervention Component |
Normal Weight |
Overweight |
Obese |
Total |
|
Control Group Observed |
||||
|
50 |
35 |
15 |
||
|
Expected |
||||
|
Calorie Counting Observed |
||||
|
70 |
20 |
10 |
||
|
Expected |
||||
|
Physical Activity Observed |
||||
|
73 |
15 |
12 |
||
|
Expected |
||||
|
Combination Observed |
||||
|
80 |
15 |
5 |
||
|
Expected |
||||
|
Total |
||||