Question

To compare the impacts of roads in two adjacent ecoregions in Brazil researchers sampled stretches of roadway over a period of 7 years in each region and recorded the species of animals killed by vehicles. In the Atlantic Forest habitat there were 178 roadkills observed, of which 51 were six-banded armadillos ( Euphractus sexcinctus). In the adjacent Cerrado habitat, there were 318 roadkills observed, of which 66 were six-banded armadillos. \({ }^{15}\) Use a chi-square test to assess the evidence that sixbanded armadillos make up different proportions of species killed for the two regions. (a) State the null hypothesis in words. (b) State the null hypothesis in symbols. (c) Compute the sample proportion of six-banded armadillos killed among roadkills in each ecosystem and display the results in a table similar to Table 10.1 .2 (d) Create a table displaying the observed and expected counts. (e) The value of \(\chi_{s}^{2}=3.948\) and the nondirectional \(P\) -value is \(0.047 .\) If \(\alpha=0.05,\) what are your conclusions? (f) Based on these findings, would it be reasonable to surmise that six-banded armadillos are in more danger of being hit at one location than the other, or is further information needed? If so, what information would be helpful?

Short answer

There is evidence to suggest that the proportions of six-banded armadillos roadkills differ between the Atlantic Forest and the Cerrado habitats, with a chi-square test statistic of 3.948 and a p-value of 0.047. Additional information on armadillo populations and behaviors is needed to further assess the danger levels at each location.

Step-by-step solution

State the Null Hypothesis in Words

The null hypothesis, in words, is that there is no difference in the proportion of six-banded armadillos killed on roads between the Atlantic Forest habitat and the adjacent Cerrado habitat.

State the Null Hypothesis in Symbols

The null hypothesis in symbols is expressed as: ewline H0: p1 = p2 ewline where p1 is the proportion of six-banded armadillos killed among roadkills in the Atlantic Forest and p2 is the proportion of those killed among roadkills in the Cerrado.

Compute the Sample Proportions

Calculate the sample proportions for six-banded armadillos in both habitats. For the Atlantic Forest, the proportion is 51 roadkills of armadillos out of 178 total roadkills. For the Cerrado, the proportion is 66 out of 318. ewline p1 = 51 / 178 ewline p2 = 66 / 318

Display Sample Proportions in a Table

Create a table to display the computed sample proportions: ewline | Habitat | Roadkills | Armadillo Roadkills | Proportion | | Atlantic Forest | 178 | 51 | p1=0.2865 | | Cerrado | 318 | 66 | p2=0.2075 |

Create a Table of Observed and Expected Counts

Expected counts are calculated assuming the null hypothesis is true, where the total number of armadillo roadkills is spread proportionally to the number of roadkills in each region. Given that there are a total of 496 roadkills and 117 are armadillos, calculate expected armadillo roadkills if the proportion were the same in both regions. With equal proportions, the expected value for each region would be (117/496) times the total roadkills in that region. ewline | Habitat | Observed Armadillions | Expected Armadillos | | Atlantic Forest | 51 | (117/496) * 178 | | Cerrado | 66 | (117/496) * 318 |

Chi-Square Test Results

Given the chi-square statistic ewline \(\chi^2_s = 3.948\) with a p-value of 0.047 and an \(\alpha = 0.05\), compare the p-value to \(\alpha\). Since the p-value is less than \(\alpha\), we reject the null hypothesis.

Conclusion and Further Information Needed

Since the null hypothesis is rejected, we conclude that there is evidence of different proportions of six-banded armadillos being killed in the two ecoregions. However, to make a more definitive claim about the dangers for armadillos at each location, additional information may be needed, such as the total populations of armadillos in each area, traffic density, road lengths, and armadillo behaviors that could affect roadkill rates.

Key concepts

Null Hypothesis

When researchers set out to understand the impact of roads on wildlife, they often use the concept of a null hypothesis. In our case, the null hypothesis is a statement suggesting that there is no significant difference between the proportions of six-banded armadillos killed on the roads in two different ecoregions in Brazil. This hypothesis serves as a default position that there is no effect or association, until evidence suggests otherwise.

In symbols, the null hypothesis for the chi-square test comparing the two ecoregions would be expressed as: \[ H_0: p_1 = p_2 \]Where \( p_1 \) represents the proportion of armadillo roadkills in the Atlantic Forest and \( p_2 \) the proportion in the Cerrado habitat. Rejecting the null hypothesis typically implies that there is a statistically significant difference between the two proportions, prompting further investigation into the factors that might be contributing to this discrepancy.

Sample Proportion

Sample proportion is a fundamental concept in statistics, representing a fraction of the sample that exhibits a particular trait. In our ecological study, the sample proportions are the number of six-banded armadillo roadkills divided by the total number of roadkills in each ecoregion. Calculating these proportions is crucial as they allow us to compare the impact of roads on this species between the Atlantic Forest and Cerrado areas.

For example, we calculated the sample proportion of armadillo roadkills as follows:\[ p_1 = \frac{51}{178} \approx 0.2865 \]in the Atlantic Forest, and\[ p_2 = \frac{66}{318} \approx 0.2075 \]in the Cerrado. These proportions are crucial for the chi-square test, which assesses whether the observed differences in proportions are significant or could have occurred by random chance.

Species Conservation

Species conservation is a critical area of environmental science that deals with efforts to protect species from extinction or population decline. Understanding the impact of human activities, such as road constructions, on wildlife species is vital for creating effective conservation strategies. The roadkill data we analyze can offer insights into the risks that roads pose to species like the six-banded armadillos.

By measuring and analyzing the impact of roadkill on armadillos, conservationists can gauge the magnitude of the threat roads pose to these animals and identify areas that may require mitigation strategies such as wildlife crossings, traffic calming measures, or habitat restoration. It's a step forward in fostering a balance between infrastructural development and biodiversity preservation, especially in biodiversity-rich ecoregions.

Ecoregion Impact Assessment

Ecoregion impact assessment is an approach used to evaluate human impacts on specific geographic areas with distinct environmental conditions and species compositions. In the context of our study, an ecoregion impact assessment helps in determining how roads affect wildlife populations differently in the Atlantic Forest and the Cerrado ecoregions.

An extensive assessment would consider not only the sample proportions of roadkill but also additional factors such as the varying ecological characteristics, traffic volume, road design, and animal behavior patterns. High-quality impact assessments are essential in developing tailored conservation efforts and policies that minimize negative outcomes for wildlife in different ecoregions. By understanding and mitigating these impacts, we help preserve the ecological integrity and resilience of these habitats for future generations.