Q. 3.1 - The Practice of Statistics for AP

Question

$\begin{array}{|ccc|}\hline \text{ Use Facebook }& \text{ Main Campus }& \text{ Common wealth }\\ \text{ Several times a month or less }& 55& 76\\ \text{ At least once a week }& 215& 157\\ \text{ At least once a day }& 640& 394\\ \text{ Total Facebook users }& \mathbf{910}& \mathbf{627}\\ \hline\end{array}$

Use Table C to find the $p$-value. Then use your calculator’s ${\chi }^2\mathrm{cdf}$ command. 

Step-by-Step Solution

Answer

The value is $0.000059$.

Step 1: Given Information

$\begin{array}{|ccc|}\hline \text{ Use Facebook }& \text{ Main Campus }& \text{ Common wealth }\\ \text{ Several times a month or less }& 55& 76\\ \text{ At least once a week }& 215& 157\\ \text{ At least once a day }& 640& 394\\ \text{ Total Facebook users }& \mathbf{910}& \mathbf{627}\\ \hline\end{array}$

Step 2: Explanation

The degree of freedom is calculated as:

$\text{Degree of freedom} =( Number of rows-1) (Number of columns-1)$

$$\begin{gathered} =(3-1)(2-1) \\ =2 \end{gathered}$$

The $p$-value at $2$ degree of freedom using table C is:

$P-\text{ value }=P\left({\chi }^2>|19.49|\right)$

$=0.000059$

Now, the $p$-value using calculator is calculated as:

Thus, the required $p$-value is $0.000059$.