## Questions and Answers

Match the types of values in a Chi-squared test with their descriptions:

Observed values = Actual data from the experiment Expected values = Theoretical data based on the null hypothesis Calculated values = Results from the Chi-squared equation Critical values = Values from the Chi-squared distribution table

Match the components of a Chi-squared test with their purposes:

Degrees of freedom = Determines the number of rows and columns Chi-squared value = Compares to the critical value for significance Null hypothesis = States there is no association between variables Alternative hypothesis = States there is an association between variables

Match the steps in a Chi-squared test with their descriptions:

Calculate the Chi-squared value = Using the observed and expected values Determine the degrees of freedom = Calculating rows and columns minus one Compare to the critical value = Using the Chi-squared distribution table Reject or fail to reject the null hypothesis = Based on the Chi-squared value and critical value

Match the concepts in a Chi-squared test with their definitions:

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Match the Chi-squared test results with their conclusions:

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Match the types of errors in a Chi-squared test with their descriptions:

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Match the Chi-squared test assumptions with their descriptions:

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Match the Chi-squared test applications with their descriptions:

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Match the Chi-squared test statistics with their formulas:

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Match the conclusions of a Chi-squared test with their interpretations:

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Match the Chi-squared test limitations with their descriptions:

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## Study Notes

### Population Dynamics

- Population growth curves can be modeled using sigmoid curves, which show an initial phase of rapid growth, followed by a plateau as the population reaches its carrying capacity.
- Carrying capacity is the maximum population size that an environment can support, and is influenced by density-dependent factors such as competition for limited resources, predation, and disease.
- Density-independent factors, such as natural disasters, can also affect population growth.

### Modeling Population Growth

- Exponential growth occurs in the initial phases of population growth, but is eventually limited by density-dependent factors.
- The sigmoid growth curve can be modeled using a graph with a logarithmic scale for population size and a non-logarithmic scale for time.

### Communities and Ecosystems

- A community consists of all the interacting populations in an ecosystem, including plants, animals, fungi, and bacteria.
- Intraspecific competition occurs between individuals of the same population, while interspecific competition occurs between different populations.
- Mutualism is a type of interspecific relationship where both species benefit, such as in the relationship between Rhizobium bacteria and legume plants.

### Estimating Population Size

- The Lincoln Index can be used to estimate population size using capture-mark-release-recapture data.
- The formula for the Lincoln Index is:
`N = (n1 * n2) / n3`

, where`n1`

is the number of individuals marked and released,`n2`

is the number of individuals recaptured, and`n3`

is the number of marked individuals recaptured.

### Interspecific Relationships

- Mutualism: Rhizobium bacteria and legume plants have a mutualistic relationship where the bacteria fix nitrogen for the plant, and the plant provides the bacteria with carbohydrates.
- Mycorrhizae: fungi form symbiotic relationships with plant roots, providing nutrients in exchange for carbohydrates.
- Zooxanthellae: coral polyps have a mutualistic relationship with algae that provide nutrients.

### Competition for Resources

- Invasive species can outcompete endemic species for resources, leading to a decrease in population size.
- Examples of invasive species include Japanese Knotweed, Box-tree caterpillar, and Himalayan Balsam.

### Testing for Association

- The Chi-squared test can be used to test for association between two species.
- The test calculates the expected frequencies of each combination of species, and compares them to the observed frequencies.
- If the calculated Chi-squared value is greater than the critical value, the null hypothesis of no association is rejected.

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## Description

This quiz covers the concepts of density-independent and density-dependent factors that affect population growth, including competition for limited resources and negative feedback control of population size.