A city transport planner is investigating the transport modes used by commuters traveling to the city center. Historically, the expected ratio of transport modes is Train : Bus : Bicycle : Walk = 9:5:1:19:5:1:19:5:1:1.
In a recent survey of 320320320 randomly selected commuters, the observed numbers for each mode of transport were:
Use the chi-squared formula
χ2=∑(O−E)2E\chi^2 = \sum \frac{(O - E)^2}{E}χ2=∑E(O−E)2to calculate the χ2\chi^2χ2 value for these data.
State the number of degrees of freedom for this test.
Using the critical values table below (for p=0.05p = 0.05p=0.05), determine whether the null hypothesis (that there is no significant difference between the observed and expected distributions) should be accepted or rejected, and explain your answer.
| Degrees of freedom | Critical value (p=0.05p = 0.05p=0.05) |
|---|---|
| 1 | 3.84 |
| 2 | 5.99 |
| 3 | 7.82 |
| 4 | 9.49 |
