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?
Show Hint
Check whether each pair of confidence intervals overlaps; overlapping intervals mean no evidence of a difference, non-overlapping intervals mean a real difference.
There is no evidence that the survival rates of social species are different between undisturbed and disturbed habitats
Solitary species have lower survival in disturbed habitats
There is no evidence that the survival rates of social and solitary species are different from each other in undisturbed habitats
There is no evidence that the survival rates of social and solitary species are different in disturbed habitats
Show Solution
The Correct Option isA, B, C
Solution and Explanation
Step 1: List the four numbers straight off the graph.
Social, undisturbed: about $0.60$, interval $[0.51, 0.69]$. Social, disturbed: about $0.58$, interval $[0.52, 0.64]$. Solitary, undisturbed: about $0.62$, interval $[0.56, 0.68]$. Solitary, disturbed: about $0.30$, interval $[0.23, 0.37]$.
Step 2: Set the overlap rule once.
Two group means are treated as statistically indistinguishable at $\alpha=0.05$ if their 95% confidence intervals overlap; if the intervals are cleanly separated with no shared range, the groups are treated as genuinely different.
Step 3: Test social, undisturbed versus social, disturbed.
$[0.51,0.69]$ and $[0.52,0.64]$ share almost the whole range $[0.52,0.64]$. They overlap, so option (A)'s claim of no evidence of a difference holds up.
Step 4: Test solitary, undisturbed versus solitary, disturbed.
$[0.56,0.68]$ and $[0.23,0.37]$ share no values at all, since $0.37 < 0.56$. They do not overlap, so solitary species really do survive worse when disturbed, confirming option (B).
Step 5: Test social versus solitary in the undisturbed habitat.
$[0.51,0.69]$ and $[0.56,0.68]$ overlap almost completely. No evidence of a difference here, confirming option (C).
Step 6: Test social versus solitary in the disturbed habitat.
$[0.52,0.64]$ and $[0.23,0.37]$ share no values, since $0.37 < 0.52$. These two are clearly different, which means option (D) is false, since it wrongly claims no evidence of a difference here.
Step 7: Collect the results.
Options (A), (B), and (C) all check out under the overlap rule, while (D) fails, since social and solitary species diverge sharply once the habitat is disturbed.
\[ \boxed{\text{(A), (B), (C)}} \]
