Question

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:

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:

1. H₀: Intervention component and weight status are not independent.

H₁: The null hypothesis is not false.

2. H₀: Intervention component and weight status are independent.

H₁: The null hypothesis is false.

3. H₀: Intervention component and weight status are independent.

H₁: The null hypothesis is not false.

4. H₀: Intervention component and weight status are not independent.

H₁: The null hypothesis is false.

The equation is supplied below, but indicate WHAT TYPE of Chi-square test you need to conduct:

χ² =(sigma)O-E² / E  

1. Goodness-of-Fit Test
2. Test of Independence

Indicate the decision rule:

1. Reject H₀ if H₀ if χ² > 21.03
2. Reject H₀ if H₀ if χ² < 18.31
3. Reject H₀ if χ² < 12.59
4. Reject H₀ if H₀ if χ² > 12.59
5. Some other answer; indicate:

Compute the expected (E) number of students for each category:

Compute the test statistic and indicate the outcome:

1. 24.974
2. 0.428
3. 5.227
4. 11.73
5. Some other answer; indicate:

True or false: We DO NOT have statistically significant evidence at α=0.05 to show that intervention component and weight status are not independent.

1. True
2. False

Indicate the most accurate p-value associated with the above-mentioned conclusion:

1. p = not significant
2. p = 0.01
3. p = 0.005
4. p < 0.005
5. Some other answer; indicate:

Answer 1

	Column 1	Column 2	Column 3	Total
Row 1	50	35	15	100
Row 2	70	20	10	100
Row 3	73	15	12	100
Row 4	80	15	5	100
Total	273	85	42	400

Null and alternative hypothesis:

Answer B.

H0: Intervention component and weight status are independent.
H1: The null hypothesis is false.

Type of chi square:

Answer B : Test of independence

Critical value:

At = 0.05 and df =(4-1)(3-1) =6, critical value, =CHISQ.INV.RT(0.05, 6) = 12.59

Decision rule:

Answer D : Reject H0 if > 12.59

Expected number(E) :

table with squared distance:

Test statistic:

Answer: A.

e: Answer B. False.

p-value = CHISQ.DIST.RT(24.974, 6) = 0.0003

Answer D