5 In an investigation into the possible relationship between smoking and weight in adults in a particular country, a researcher selected a random sample of 500 adults.
The adults in the sample were classified according to smoking status (non-smoker, light smoker or heavy smoker, where light smoker indicates less than 10 cigarettes per day) and body weight (underweight, normal weight or overweight).
Fig. 5 is a screenshot showing part of the spreadsheet used to calculate the contributions for a chisquared test. Some values in the spreadsheet have been deliberately omitted.
\begin{table}[h]
| A | B | C | D | E | F |
| 1 | Observed frequencies |
| 2 | | Underweight | Normal | Overweight | Totals | |
| 3 | Non-smoker | 8 | 52 | 178 | 238 | |
| 4 | Light smoker | 10 | 40 | 68 | 118 | |
| 5 | Heavy smoker | 5 | 47 | 92 | 144 | |
| 6 | Totals | 23 | 139 | 338 | 500 | |
| 7 | | | | | | |
| 8 | Expected frequencies | | |
| 9 | Non-smoker | 10.9480 | 66.1640 | 160.8880 | | |
| 10 | Light smoker | 5.4280 | | 79.7680 | | |
| 11 | Heavy smoker | | 40.0320 | 97.3440 | | |
| 12 | | | | | | |
| 13 | |
| 14 | Non-smoker | 0.7938 | | 1.8200 | | |
| 15 | Light smoker | 3.8510 | 1.5785 | 1.7361 | | |
| 16 | Heavy smoker | 0.3982 | 1.2129 | 0.2934 | | |
| 17 | | | | | | |
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{table}
- Showing your calculations, find the missing values in each of the following cells.
- B11
- C10
- C14
- Complete the hypothesis test at the \(1 \%\) level of significance.
- For each smoking status, give a brief interpretation of the largest of the three contributions to the test statistic.