3 A student wants to know whether there is any association between age and whether or not people smoke. The student takes a sample of 120 adults and asks each of them whether or not they smoke. Below is a screenshot showing part of a spreadsheet used to analyse the data. Some values in the spreadsheet have been deliberately omitted.
| A | B | C | D | E |
| 1 | \multirow{3}{*}{} | Observed frequency |
| 2 | | | Age |
| 3 | | | 16-34 | 35-59 | 60 and over |
| 4 | \multirow{2}{*}{Smoking status} | Smoker | 13 | 7 | 3 |
| 5 | | Non-smoker | 28 | 43 | 26 |
| 6 | | | |
| 7 | | | Expected frequency |
| 8 | | | 7.8583 | | |
| 9 | | | 33.1417 | | |
| 10 | | | |
| 11 | | | Contributions to the test statistic |
| 12 | | | 3.3642 | 0.6964 | 1.1775 |
| 13 | | | | 0.1651 | 0.2792 |
| 11 | | | | | |
- The student wants to carry out a chi-squared test to analyse the data.
State a requirement of the sample if the test is to be valid.
For the rest of this question, you should assume that this requirement is met.
- Determine the missing values in each of the following cells.
- E8
- C13
- In this question you must show detailed reasoning.
Carry out a hypothesis test at the \(5 \%\) significance level to investigate whether there is any association between age and smoking status. - Discuss what the data suggest about the smoking status for each different age group.