9.9 Optional: \(P\)-values

This question is optional; e.g., if you need more practice, or you are studying for the exam.

(Answers available in Sect. A.10)

An ecologist is studying two different grasses to help combat soil salinity, by comparing to a new grass (Grass A) to a native grass (Grass B). She uses \(50\) different sites, allocating the two grasses at random to the sites (\(25\) sites for each grass).

After \(12\) months, the ecologist records whether the soil salinity at each site has improved, and hence computes the odds that each grass will improve the salinity. She finds a statistically significant difference between the odds in the two groups. Which of these statements is consistent with this conclusion?

The \(\text{OR} = 4.1\) and \(P = 0.36\)
Consistent with conclusion NOT consistent with conclusion
The \(\text{OR} = 4.1\) and \(P = 0.0001\)

Consistent with conclusion NOT consistent with conclusion
The \(\text{OR} = 0.91\) and \(P = 0.36\)

Consistent with conclusion NOT consistent with conclusion
The \(\text{OR} = 0.91\) and \(P = 0.0001\)

Consistent with conclusion NOT consistent with conclusion

How would the other statements be interpreted then?