### Understanding Chi-Square Test#### Example 12.2.3-TThis example features a table that displays observed values and expected values (in parentheses) for two categorical variables, $ X $ and $ Y $. Variable $ X $ is divided into three categories ($ X_1, X_2, X_3 $), and variable $ Y $ consists of two categories ($ Y_1, Y_2 $). #### Data Table:| | $ X_1 $ | $ X_2 $ | $ X_3 $ ||-------|--------|--------|--------|| $ Y_1 $ | 32 (35.39) | 44 (44.42) | 51 (47.19) || $ Y_2 $ | 19 (15.61) | 20 (19.58) | 17 (20.81) |#### Task:(a) Compute the value of the chi-square test statistic.\[ \chi^2_0 = \text{[Round to three decimal places as needed.]} \]In this example, you'll calculate the chi-square test statistic to test the association between the categories of $ X $ and $ Y $.### Explanation:Each cell in the table contains two numbers: the observed count and, in parentheses, the expected count under the assumption that there is no association between $ X $ and $ Y $. The chi-square statistic is computed based on the differences between these observed and expected values.

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Description: ### Understanding Chi-Square Test#### Example 12.2.3-TThis example features a table that displays observed values and expected values (in parentheses) for two categorical variables, $ X $ and $ Y $. Variable $ X $ is divided into three categor

The given data is, Observed values x1 x2 x3 y1 32 44 51 y2 19 20 17 Expected values x1 x2 x3 y1 35.39 44.42 47.19 y2 15.61 19.58 20.81a) The chi-square test statistic is, X02 =Σ{(observed value-Expected value)2Expected value} 0.324727 0.003971 0.30761 0.736201 0.009009 0.697554 X02=2.0790 The value of the chi-square test statistic is 2.079

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= Question Help The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has wo categories. Use the table to complete parts (a) and (b) below. X, X2 X, P 32 51 (35.39)(44.42)(47.19) 19 20 44 17 (15.61)(19.58)(20.81) Y2 a) Compute the value of the chi-square test statistic. (Round to three decimal places as needed.)

= Question Help The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has wo categories. Use the table to complete parts (a) and (b) below. X, X2 X, P 32 51 (35.39)(44.42)(47.19) 19 20 44 17 (15.61)(19.58)(20.81) Y2 a) Compute the value of the chi-square test statistic. (Round to three decimal places as needed.)

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### Understanding Chi-Square Test

#### Example 12.2.3-T

This example features a table that displays observed values and expected values (in parentheses) for two categorical variables, $ X $ and $ Y $. Variable $ X $ is divided into three categories ($ X_1, X_2, X_3 $), and variable $ Y $ consists of two categories ($ Y_1, Y_2 $).

#### Data Table:

| | $ X_1 $ | $ X_2 $ | $ X_3 $ |
|-------|--------|--------|--------|
| $ Y_1 $ | 32 (35.39) | 44 (44.42) | 51 (47.19) |
| $ Y_2 $ | 19 (15.61) | 20 (19.58) | 17 (20.81) |

#### Task:

(a) Compute the value of the chi-square test statistic.

\[ \chi^2_0 = \text{[Round to three decimal places as needed.]} \]

In this example, you'll calculate the chi-square test statistic to test the association between the categories of $ X $ and $ Y $.

### Explanation:

Each cell in the table contains two numbers: the observed count and, in parentheses, the expected count under the assumption that there is no association between $ X $ and $ Y $. The chi-square statistic is computed based on the differences between these observed and expected values.

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