Question: 15. A researcher investigates whether there is an association between regular exercise and preferred mode of transport to work. A survey of 500 people produces the following two-way frequency table:
Mode of transport Exercises regularly Does not exercise regularly Total
Car 120 180 300
Public transport 90 50 140
Active (walk/bike) 40 20 60
Total 250 250 500
Using appropriate percentages, determine whether there is an association between exercising regularly and mode of transport. Justify your conclusion.
1. **State the problem:** We want to determine if there is an association between exercising regularly and the preferred mode of transport to work using the given frequency table.
2. **Understand the data:** The table shows counts of people by mode of transport and whether they exercise regularly or not.
3. **Calculate row percentages (percentage within each mode of transport):**
- For Car: $$\frac{120}{300} \times 100 = 40\%$$ exercise regularly, $$\frac{180}{300} \times 100 = 60\%$$ do not exercise regularly.
- For Public transport: $$\frac{90}{140} \times 100 \approx 64.29\%$$ exercise regularly, $$\frac{50}{140} \times 100 \approx 35.71\%$$ do not exercise regularly.
- For Active (walk/bike): $$\frac{40}{60} \times 100 = 66.67\%$$ exercise regularly, $$\frac{20}{60} \times 100 = 33.33\%$$ do not exercise regularly.
4. **Calculate column percentages (percentage within exercise groups):**
- Among those who exercise regularly (total 250):
- Car: $$\frac{120}{250} \times 100 = 48\%$$
- Public transport: $$\frac{90}{250} \times 100 = 36\%$$
- Active: $$\frac{40}{250} \times 100 = 16\%$$
- Among those who do not exercise regularly (total 250):
- Car: $$\frac{180}{250} \times 100 = 72\%$$
- Public transport: $$\frac{50}{250} \times 100 = 20\%$$
- Active: $$\frac{20}{250} \times 100 = 8\%$$
5. **Interpretation:**
- A higher percentage of people who use public transport or active modes exercise regularly compared to car users.
- Car users have a lower percentage exercising regularly (40%) compared to public transport (64.29%) and active modes (66.67%).
- Among non-exercisers, a larger proportion use cars (72%) compared to public transport (20%) and active modes (8%).
6. **Conclusion:** There appears to be an association between exercising regularly and mode of transport. People who use public transport or active modes are more likely to exercise regularly than car users.
This conclusion is justified by the differing percentages across modes of transport within exercise groups, indicating the variables are not independent.