6. An online survey on the use of social media asked the following question:
\begin{displayquote}
"Do you use any form of social media?"
\end{displayquote}
The results for a total of 1953 respondents are shown in the table below.
| Age in years | |
| Use social media | 18-29 | 30-49 | 50-64 | 65 or older | Total |
| Yes | 310 | 412 | 348 | 196 | 1266 |
| No | 42 | 116 | 196 | 333 | 687 |
| Total | 352 | 528 | 544 | 529 | 1953 |
To test whether there is a relationship between social media use and age, a significance test is carried out at the \(5 \%\) level.
- State the null and alternative hypotheses.
- Show how the expected frequency \(228 \cdot 18\) is calculated in the table below.
| Expected values | Age in years |
| Use social media | 18-29 | 30-49 | 50-64 | 65 or older |
| Yes | \(228 \cdot 18\) | \(342 \cdot 27\) | 352.64 | 342.92 |
| No | 123.82 | 185.73 | 191.36 | 186.08 |
- Determine the value of \(s\) in the table below.
| Chi-squared contributions | Age in years |
| Use social media | 18-29 | 30-49 | 50-64 | 65 or older |
| Yes | 29.34 | \(s\) | 0.06 | 62.94 |
| No | 54.07 | 26-18 | 0.11 | 115.99 |
- Complete the significance test, showing all your working.
- A student, analysing these data on a spreadsheet, obtains the following output.
\includegraphics[max width=\textwidth, alt={}, center]{77fd7ad7-f5a3-4947-afc6-e5ef45bef7a8-5_202_1271_445_415}
Explain why the student must have made an error in calculating the \(p\)-value.