5 A random sample of workers for a large company were asked whether they are smokers, ex-smokers or have never smoked. The responses were classified by the type of worker: Managerial, Production line or Administrative.
Fig. 5 is a screenshot showing part of the spreadsheet used to analyse the data. Some values in the spreadsheet have been deliberately omitted.
\begin{table}[h]
| A | B | C | D | E | F |
| 1 | Observed frequencies | |
| 2 | | Smoker | Ex-smoker | Never smoked | Totals | |
| 3 | Managerial | 2 | 10 | 5 | 17 | |
| 4 | Production line | 18 | 15 | 21 | 54 | |
| 5 | Administrative | 13 | 6 | 14 | 33 | |
| 6 | Totals | 33 | 31 | 40 | 104 | |
| 7 | |
| 8 | | Expected frequencies | | |
| 9 | | 5.3942 | 5.0673 | 6.5385 | | |
| 10 | | 17.1346 | | 20.7692 | | |
| 11 | | 10.4712 | 9.8365 | 12.6923 | | |
| 12 | | | | |
| 13 | | Contributions to the test statistic | | |
| 14 | | 2.1358 | 4.8017 | 0.3620 | | |
| 15 | | 0.0437 | | 0.0026 | | |
| 16 | | | 1.4964 | 0.1347 | | |
| 17 | | | | Test statistic | 9.66 | |
| 18 | | | | | | |
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{table}
- (A) State the sample size.
(B) State the null and alternative hypotheses for a test to investigate whether there is any association between type of worker and smoking status. - Showing your calculations, find the missing values in each of the following cells.
- C 10
- C 15
- B 16
- Complete the hypothesis test at the \(10 \%\) level of significance.
- Discuss briefly what the data suggest about smoking status for different types of workers. You should make a comment for each type of worker.