Question

In a study of eating disorders among adolescent girls, a researcher asked each of the subjects whether they would prefer to gain weight, lose weight, or maintain their present weight. For White girls: 34 want to reduce weight, 66 would like to maintain weight, and 31 want to gain weight; For African- American girls: 23 want to reduce weight, 44 would like to maintain weight, 68 want to gain weight.

You are asked to examine whether race influences adolescent girls' attitude towards their weight, i.e. Perform the following:

a. State the hypotheses (4pts)
b. Set up the contingency table, along with the marginal row and marginal column (10pts)
c. Use the 6-steps hypothesis test to determine whether race influences attitude towards weight(26pts)

Answer 1

Chi-square test of independence

Solution:

Part a

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H₀: Race does not influence attitude towards weight.

Alternative hypothesis: H_a: Race influences attitude towards weight.

Part b

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	Reduce weight	maintain weight	Gain weight	Total
White Girls	34	66	31	131
African American Girls	23	44	68	135
Total	57	110	99	266

Part c

We assume level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 2

Number of columns = c = 3

Degrees of freedom = df = (r – 1)*(c – 1) = 1*2 = 2

α = 0.05

Critical value = 5.991464547

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	Reduce weight	maintain weight	Gain weight	Total
White Girls	34	66	31	131
African American Girls	23	44	68	135
Total	57	110	99	266

Expected Frequencies
	Column variable
Row variable	Reduce weight	maintain weight	Gain weight	Total
White Girls	28.07142857	54.17293233	48.7556391	131
African American Girls	28.92857143	55.82706767	50.2443609	135
Total	57	110	99	266

Calculations
(O - E)
5.928571	11.82707	-17.7556
-5.92857	-11.8271	17.75564

(O - E)^2/E
1.25209	2.582093	6.46618
1.214991	2.505586	6.274589

Chi square = ∑[(O – E)^2/E] = 20.29552888

P-value = 0.0000392

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that Race influences attitude towards weight.