8 An insurance company groups its vehicle insurance policies into two categories, car insurance and motorbike insurance.
The number of claims in a random sample of 80 policies was monitored and the results summarised in contingency Table 1.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Table 1}
| \multirow{2}{*}{} | Number of claims |
| | 0 | 1 | 2 | 3 or more | Total |
| \multirow[b]{3}{*}{Type of insurance policy} | Car | 9 | 10 | 11 | 5 | 35 |
| Motorbike | 19 | 13 | 8 | 5 | 45 |
| Total | 28 | 23 | 19 | 10 | 80 |
\end{table}
The insurance company decides to carry out a \(\chi ^ { 2 }\)-test for association between number of claims and type of insurance policy using the information given in Table 1.
8
- The contingency table shown in Table 2 gives some of the exact expected frequencies for this test.
Complete Table 2 with the missing exact expected values.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Table 2}
| \multirow{2}{*}{} | Number of claims |
| | 0 | 1 | 2 | 3 or more |
| \multirow{2}{*}{Type of insurance policy} | Car | | 10.0625 | | 4.375 |
| Motorbike | | | 10.6875 | |
- Carry out the insurance company's test, using the \(10 \%\) level of significance.
\includegraphics[max width=\textwidth, alt={}, center]{313cd5ce-07ff-4781-a134-565b8b221145-12_2488_1719_219_150}
Additional page, if required.
Write the question numbers in the left-hand margin.
Additional page, if required.
Write the question numbers in the left-hand margin.
Additional page, if required.
Write the question numbers in the left-hand margin.