Question

In: Statistics and Probability

A team of researchers wanted to assess the effectiveness of the 4 components of a weight...

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.

Indicate the correct competing hypotheses: (1pt)

H0: Intervention component and weight status are not independent.

H1: The null hypothesis is not false.

H0: Intervention component and weight status are independent.

H1: The null hypothesis is false.

H0: Intervention component and weight status are independent.

H1: The null hypothesis is not false.

H0: Intervention component and weight status are not independent.

H1: The null hypothesis is false.

Solutions

Expert Solution

The null and alternative hypothesis is

H0: intervention component and weight status independent.

H1: intervention component and weight status not independent.

Test statistic is

O: Observed frequency
E: Expected frequency.

E = ( Row total*Column total) / Grand total

O E (O-E) (O-E)^2 (O-E)^2/E
50 68.25 -18.25 333.0625 4.880037
35 21.25 13.75 189.0625 8.897059
15 10.5 4.5 20.25 1.928571
70 68.25 1.75 3.0625 0.044872
20 21.25 -1.25 1.5625 0.073529
10 10.5 -0.5 0.25 0.02381
73 68.25 4.75 22.5625 0.330586
15 21.25 -6.25 39.0625 1.838235
12 10.5 1.5 2.25 0.214286
80 68.25 11.75 138.0625 2.022894
15 21.25 -6.25 39.0625 1.838235
5 10.5 -5.5 30.25 2.880952
Total 24.973

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 4 - 1) * (3 - 1) = 3 * 2 = 6

Level of signfiicance = 0.05

Critical value = 12.592

Test statistic > critical value we reject null hypothesis.

Conclusion: Intervention component and weight status are not independent.

orchestra answered 1 year ago
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