Question

Gender and Frequency of Status Updates on Facebook Exercise 7.48 introduces a study about users of social networking sites such as Facebook. Table 7.36 shows the self-reported frequency of status updates on Facebook by gender. Are frequency of status updates and gender related? Show all details of the test. $$ \begin{array}{l|rr|r} \hline \text { IStatus/Gender } \rightarrow & \text { Male } & \text { Female } & \text { Total } \\ \hline \text { Every day } & 42 & 88 & 130 \\ \text { 3-5 days/week } & 46 & 59 & 105 \\ \text { 1-2 days/week } & 70 & 79 & 149 \\ \text { Every few weeks } & 77 & 79 & 156 \\ \text { Less often } & 151 & 186 & 337 \\ \hline \text { Total } & 386 & 491 & 877 \\ \hline \end{array} $$

Short answer

Use the chi-square test to calculate the p-value and compare it with the significance level. If p-value is smaller than 0.05, reject the null hypothesis and conclude that there is a significant relationship between gender and the frequency of status updates on Facebook. The exact p-value, however, depends on the calculated chi-square statistic.

Step-by-step solution

State the null and alternate hypothesis

The Null hypothesis, \(H_0\), is that there is no relationship between the gender of the user and the frequency of Facebook updates. The Alternative hypothesis, \(H_a\), is that there is a relationship between the gender of the user and the frequency of Facebook updates.

Calculate the expected frequencies

The expected frequency for each cell in the table is calculated using the formula: \((\text{row total} * \text{column total}) / \text{grand total}\). Do this for each cell in the table.

Compute the chi-square statistics

The Chi-Square statistic is calculated as: \(\chi^2 = \sum \frac{(O - E)^2}{E}\), where O refers to the observed frequency and E refers to the expected frequency. Compute this value using the observed and expected frequencies for each cell.

Determine the degrees of freedom

Degrees of freedom for this test is calculated as: \((\text{number of rows} - 1) * (\text{number of columns} - 1)\). In this case, we have 5 rows and 2 columns, so the degrees of freedom is \((5 - 1) * (2 - 1) = 4\)

Obtain the p-value and draw conclusion

The p-value can be obtained from a Chi-Square distribution table using the computed chi-square statistic and the degrees of freedom. If the p-value is smaller than the significance level (often 0.05), we reject the null hypothesis and conclude there is a relationship between the gender and frequency of status updates.