Conditional probability and relative risk from a two-way table
kaimoana / public health
A regional council tested 400 samples of shellfish (tuatua and pipi) collected at popular harvesting sites. Each sample was classified by whether it was collected within 1 km of a stormwater outlet and whether it tested positive for norovirus. The results are in the table and in Figure 1.
| | Positive | Negative | Total |
|---|---|---|---|
| Within 1 km of outlet | 48 | 112 | 160 |
| More than 1 km from outlet | 21 | 219 | 240 |
| Total | 69 | 331 | 400 |
Stacked horizontal bar chart of the number of shellfish samples testing positive and negative for norovirus, for the 160 samples within 1 km of a stormwater outlet and the 240 samples more than 1 km away.Facts you may need
(a)
Calculate the probability that a sample collected within 1 km of an outlet tested positive.
(b)
Calculate the relative risk of a positive test for samples within 1 km compared with samples further away, and interpret it.
(c)
A media release states: '70% of contaminated shellfish come from within 1 km of stormwater outlets, so 70% of shellfish near outlets are contaminated.' Use the table or Figure 1 to explain the error and give the correct figure.
