Question

1. You are conducting a test of independence for the claim that there is an association between the row variable and the column variable.

	X	Y	Z
A	57	25	23
B	32	35	15

What is the chi-square test-statistic for this data?
χ2=

2. You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.

Category	Population #1	Population #2
A	36	123
B	21	73

What is the chi-square test-statistic for this data?
χ2=

3.

Based on the data shown below, calculate the correlation coefficient (to three decimal places)

x	y
5	27.65
6	26.12
7	27.99
8	31.26
9	30.63
10	33.7
11	31.27
12	34.14
13	35.81
14	36.68
15	37.55

Answer 1

(1) Observed frequency = O = (57, 32, 25, 35, 23, 15).
Expected frequency = (row total * column total)/grand total = E = (50, 39, 33.7, 26.3, 21.3, 16.7).
Test statistic = sum((O-E)²/E) = 7.6604 (please round this number to the required number of decimal places)

(2) Observed frequency = O = (36, 21,123, 73).
Expected frequency = (row total * column total)/grand total = E = (35.8, 21.2, 123.2, 72.8).
Test statistic = sum((O-E)²/E) = 0.0031 (please round this number to the required number of decimal places)

(3) Correlation coefficient = Cor(x, y) = 0.956