Q.56 - The Practice of Statistics for AP

Question

The cell in the table that contributes the most to the chi-square statistic is (a) Female, $50–50$ chance. 

(b) Male, $50–50$ chance. 

(c) Female, almost certain. 

(d) Male, almost certain. 

(e) All the cells contribute equally to the test statistic. 

Step-by-Step Solution

Answer

The correct option is (d) Male, almost certain.

Step 1: Given Information

The table is

Step 2: Explanation

To determine the cell that contributes more to the test statistic that need to be computed based on the expected frequency.

The chi-square test formula is

${\chi }^2=\sum \frac{{\left(O_i-E_i\right)}^2}{E_i}$

The Expected frequency formula is given below as,

$E_i=\frac{\text{ Row total }\times \text{ Column total }}{\text{ Grand total }}$

The expected frequency for observations is calculated as follows:

$E_1=\frac{222\times 2625}{4877}$

$E_1=119.5$

Step 3: Explanation

From the above table, the last column represents the each cell contribution to test statistic.

It can be seen that $20.51$ is the largest value among them. It represents the value of Male, almost certain.

Thus, Male, almost certain cell contributes most to the test statistic.

Therefore correct option is (d) Male, almost certain.