Question

What is the value of χ2 for the two-way table?

A B C D
X 5 10 15 20
Y 7 13 17 21
(2 points)
0.5320
0.0801
1.08
0.2830
0.9632

Answer 1

0.2830

Explanation:

Observed Values

Add totals for the rows and columns to the two-way table (see attachment 1).

Expected Values

Create an "Expected Values" table by multiplying each row total by each column total and dividing by the overall total (see attachment 2).

Chi-square test statistic

`\sf ((observed-expected)^2)/(expected)`

Create a third table by using the formula to calculate the chi-square test statistic for each cell of the table (see attachments 3 and 4)

Chi-square

Add the values from the table in attachment 4.

`\sf X^2=0.05556+0.03945+0.002315+0.05465+0.04789+0.03401+0.001996+0.04711`
`\implies \sf X^2=0.2830 \:(4 \:sf)`