3 A mobile phone company offers an insurance policy to its customers when they purchase a mobile phone. The company conducted a survey on the age of the customers and whether or not claims were made.
A random sample of 1200 customers from this company was investigated for 2020 and the results are shown in the table below.
| Claim made in 2020 | No claim made in 2020 | Total |
| \multirow{3}{*}{Age} | 17-20 years | 24 | 176 | 200 |
| 21-50 years | 48 | 652 | 700 |
| 51 years and over | 14 | 286 | 300 |
| Total | 86 | 1114 | 1200 |
The data are to be used to determine whether or not making a claim is independent of age.
- Calculate the expected frequencies for the age group 51 years and over that
- made a claim in 2020
- did not make a claim in 2020
The 4 classes of customers aged between 17 and 50 give a value of \(\sum \frac { ( O - E ) ^ { 2 } } { E } = 7.123\) correct to 3 decimal places.
- Test, at the \(1 \%\) level of significance, whether or not making a claim is independent of age. Show your working clearly, stating your hypotheses, the degrees of freedom, the test statistic and the critical value used.