Question

Age and Frequency of Status Updates on Facebook Exercise 7.48 introduces a study about users of social networking sites such as Facebook. Table 7.35 shows the self-reported frequency of status updates on Facebook by age groups. (a) Based on the totals, if age and frequency of status updates are really unrelated, how many of the 156 users who are 18 to 22 years olds should we expect to update their status every day? (b) Since there are 20 cells in this table, we'll save some time and tell you that the chi-square statistic for this table is \(210.9 .\) What should we conclude about a relationship (if any) between age and frequency of status updates? $$ \begin{array}{l|rrrr|r} \hline \downarrow \text { Status/Age } \rightarrow & 18-22 & 23-35 & 36-49 & 50+ & \text { Total } \\ \hline \text { Every day } & 47 & 59 & 23 & 7 & 136 \\ \text { 3-5 days/week } & 33 & 47 & 30 & 7 & 117 \\ \text { 1-2 days/week } & 32 & 69 & 35 & 25 & 161 \\ \text { Every few weeks } & 23 & 65 & 47 & 34 & 169 \\ \text { Less often } & 21 & 74 & 99 & 170 & 364 \\ \hline \text { Total } & 156 & 314 & 234 & 243 & 947 \\ \hline \end{array} $$

Short answer

For task (a), if age and frequency of status updates were unrelated, we would expect approximately 22 (or to be exact, 22.26) users of ages 18-22 to update their status every day. For task (b), considering the high chi-square statistic, it's likely that there is a relationship between age and frequency of status updates.

Step-by-step solution

Calculate Expected Status Updates

To find the expected number of 18-22 year olds who should update their status every day if age and status updates are unrelated, the formula \(Expected = \frac{(Row \ Total)(Column \ Total)}{Total \ Population}\) is used. So, the calculation will be \( \frac{(156)(136)}{947} \)

Perform the Calculation

The calculation \( \frac{(156)(136)}{947} \) gives approximately 22.26 expected users in the 18-22 age group updating their status daily.

Interpret the Chi-Square Statistic

A chi-square statistic of \(210.9\) is considerably high. In a chi-square test, a high value typically indicates that the observed data are not in line with the expected data under the assumed null hypothesis - in this case, the hypothesis that age and frequency of status updates are unrelated. Therefore, it's likely that there is some relationship between age and frequency of updates.