- The manager of a company making ice cream believes that the proportions of people in the population who prefer vanilla, chocolate, strawberry and other are in the ratio \(10 : 5 : 2 : 3\)
The manager takes a random sample of 400 customers and records their age and favourite ice cream flavour. The results are shown in the table below.
| \multirow{2}{*}{} | Ice cream flavour | |
| | Vanilla | Chocolate | Strawberry | Other | Total |
| \multirow{3}{*}{Age} | Child | 95 | 25 | 13 | 25 | 158 |
| Teenager | 57 | 20 | 17 | 36 | 130 |
| Adult | 36 | 50 | 10 | 16 | 112 |
| Total | 188 | 95 | 40 | 77 | 400 |
- Use the data in the table to test, at the \(5 \%\) level of significance, the manager's belief. You should state your hypotheses, test statistic, critical value and conclusion clearly.
A researcher wants to investigate whether or not there is a relationship between the age of a customer and their favourite ice cream flavour. In order to test whether favourite ice cream flavour and age are related, the researcher plans to carry out a \(\chi ^ { 2 }\) test.
- Use the table to calculate expected frequencies for the group
- teenagers whose favourite ice cream flavour is vanilla,
- adults whose favourite ice cream flavour is chocolate.
- Write down the number of degrees of freedom for this \(\chi ^ { 2 }\) test.