- A business accepts cash, bank cards or mobile apps as payment methods.
The manager wishes to test whether or not there is an association between the payment amount and the payment method used.
The manager takes a random sample of 240 payments and records the payment amount and the payment method used.
The manager's results are shown in the table.
| \multirow{2}{*}{} | Payment amount |
| | Under £50 | £50 to £150 | Over £150 |
| \multirow{3}{*}{Payment method} | Cash | 23 | 19 | 18 |
| Bank card | 21 | 32 | 31 |
| Mobile app | 16 | 39 | 41 |
Using these results,
- calculate the expected frequencies for the payment amount under \(\pounds 50\) that
- use cash
- use a bank card
- use a mobile app
Given that for the other 6 classes \(\sum \frac { ( O - E ) ^ { 2 } } { E } = 2.4048\) to 4 decimal places,
- test, at the \(5 \%\) level of significance, whether or not there is evidence for an association between the payment amount and the payment method used. You should state the hypotheses, the test statistic, the degrees of freedom and the critical value used for this test.