Question

A researcher is interested in understanding whether multi-species sociality (in which species form cohesive groups with other species) plays a role in helping species cope with habitat disturbance. She estimates the survival rates of social species and solitary species in undisturbed and disturbed habitats, and these are plotted in the graph below.

Circles represent mean survival rates and error bars represent 95% confidence intervals. Based on the means and confidence intervals presented in the graph (\(\alpha = 0.05\)), which one or more of the following can be reasonably concluded?

• A. There is no evidence that the survival rates of social species are different between undisturbed and disturbed habitats
• B. Solitary species have lower survival in disturbed habitats
• C. There is no evidence that the survival rates of social and solitary species are different from each other in undisturbed habitats
• D. There is no evidence that the survival rates of social and solitary species are different in disturbed habitats

Hint:

Check whether each pair of confidence intervals overlaps; overlapping intervals mean no evidence of a difference, non-overlapping intervals mean a real difference.

Answer 1

The Correct Option is A, B, C

Step 1: Understanding the Question.
The graph plots mean survival rate with 95% confidence intervals for social and solitary species, each measured in undisturbed and disturbed habitats. We need to read off which comparisons show a real difference and which do not, using the standard rule that overlapping 95% confidence intervals mean no clear evidence of a difference at \(\alpha=0.05\).

Step 2: Key Formula or Approach.
If two confidence intervals overlap substantially, we cannot reasonably conclude the underlying means are different, since chance variation could explain the small gap. If the confidence intervals do not overlap at all, the difference is likely real.

Step 3: Compare social species across habitats.
Social species have a mean survival rate of about \(0.60\) (interval roughly \(0.51\) to \(0.69\)) in undisturbed habitat and about \(0.58\) (interval roughly \(0.52\) to \(0.64\)) in disturbed habitat. These two intervals overlap heavily, so there is no evidence that disturbance changes survival in social species. This supports option (A).

Step 4: Compare solitary species across habitats.
Solitary species have a mean survival rate of about \(0.62\) (interval roughly \(0.56\) to \(0.68\)) in undisturbed habitat, but only about \(0.30\) (interval roughly \(0.23\) to \(0.37\)) in disturbed habitat. These two intervals are far apart and do not overlap at all, so solitary species clearly survive worse in disturbed habitats. This supports option (B).

Step 5: Compare social versus solitary species in undisturbed habitat.
In the undisturbed habitat, social species sit at about \(0.60\) and solitary species sit at about \(0.62\), with heavily overlapping intervals. There is no evidence of a real difference between the two groups here. This supports option (C).

Step 6: Compare social versus solitary species in disturbed habitat.
In the disturbed habitat, social species sit at about \(0.58\) while solitary species drop to about \(0.30\), and their intervals do not overlap at all. This is a clear, real difference, so option (D), which claims there is no evidence of a difference here, is false.

Step 7: Final Answer.
The graph supports options (A), (B), and (C): social species are unaffected by disturbance, solitary species survive worse when disturbed, and social and solitary species look similar only in the undisturbed habitat.
\[ \boxed{\text{(A), (B), (C)}} \]