- A survey asked a random sample of 200 people their age and the main use of their mobile phone.
The results are shown in Table 1 below.
\begin{table}[h]
| \multirow{2}{*}{} | Main use of their mobile phone |
| | Internet | Texts | Phone calls |
| \multirow{3}{*}{Age} | Under 20 | 27 | 14 | 9 |
| From 20 to 40 | 32 | 34 | 29 |
| Over 40 | 15 | 19 | 21 |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
The data are to be used to test whether or not age and main use of their mobile phone are independent.
Table 2 shows the expected frequencies for each group, assuming people's age and main use of their mobile phone are independent.
\begin{table}[h]
| \multirow{2}{*}{} | Main use of their mobile phone |
| | Internet | Texts | Phone calls |
| \multirow{3}{*}{Age} | Under 20 | 18.5 | 16.75 | 14.75 |
| From 20 to 40 | 35.15 | 31.825 | 28.025 |
| Over 40 | 20.35 | 18.425 | 16.225 |
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{table}
- For users under 20 choosing the Internet as the main use of their mobile phone,
- verify that the expected frequency is 18.5
- show that the contribution to the \(\chi ^ { 2 }\) test statistic is 3.91 to 3 significant figures.
- Given that the \(\chi ^ { 2 }\) test statistic for the data is 9.893 to 3 decimal places, test at the \(5 \%\) level of significance whether or not age and main use of their mobile phone are independent. State your hypotheses clearly.