To determine whether there is a connection between birds having long beaks and their ability to fly, we can find the odds ratio. This odds ratio will compare the odds of birds with long beaks being able to fly against the odds of birds without long beaks being able to fly.
Let's break down the solution step by step:
1. Identify the data from the contingency table:
- Long beak and flies: [tex]\(11\)[/tex]
- Long beak and does not fly: [tex]\(3\)[/tex]
- Not long beak and flies: [tex]\(7\)[/tex]
- Not long beak and does not fly: [tex]\(13\)[/tex]
2. Calculate the odds for birds with long beaks being able to fly:
[tex]\[
\text{Odds}_{\text{long beak, fly}} = \frac{\text{Number of long beak birds that fly}}{\text{Number of long beak birds that do not fly}} = \frac{11}{3} \approx 3.67
\][/tex]
3. Calculate the odds for birds without long beaks being able to fly:
[tex]\[
\text{Odds}_{\text{not long beak, fly}} = \frac{\text{Number of not long beak birds that fly}}{\text{Number of not long beak birds that do not fly}} = \frac{7}{13} \approx 0.54
\][/tex]
4. Calculate the odds ratio:
[tex]\[
\text{Odds Ratio} = \frac{\text{Odds}_{\text{long beak, fly}}}{\text{Odds}_{\text{not long beak, fly}}} = \frac{3.67}{0.54} \approx 6.81
\][/tex]
So, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is approximately [tex]\(6.81\)[/tex]. This means that birds with long beaks are about 6.81 times more likely to fly compared to birds without long beaks.
