Question

Determine whether the data collected represents a population or a sample. Twenty animals are put on a new diet and their weight gain over 3 months is recorded.

Short answer

Answer: The data represents a sample.

Step-by-step solution

Define Population and Sample

A population refers to the entire group of individuals or items being studied. A sample, on the other hand, is a representative subset of the population.

Identify the Group Being Studied

In this exercise, the group being studied consists of animals submitted to a new diet and their weight gain over 3 months.

Determine the Size of the Group

The data consists of twenty animals. However, it's important to determine whether this includes all animals subjected to the new diet or if it's just a fraction of the total animals receiving the diet.

Consider the Context

Since the data is about a new diet and its effect on the weight gain of animals, it is highly likely there are more animals that have or will receive the new diet than just the twenty animals included in the data. The context indicates that the group of animals receiving the new diet is likely bigger than those twenty included.

Conclusion

Given that the data collected represents only a subset of animals receiving the new diet, rather than the entire group, we can conclude that the data represents a sample rather than a population.

Key concepts

Statistical Analysis

Statistical analysis involves examining data to uncover patterns, trends, and relationships. Understanding whether the dataset represents a population or a sample is crucial for accurate analysis. A population includes the entire set of entities, while a sample is a smaller group selected from this larger set.

When analyzing data, statisticians use different approaches depending on whether they are dealing with a sample or a whole population.

• If the dataset is a population, calculations like the mean, variance, and standard deviation are straightforwardly representative.
• For samples, statisticians often use inferential statistics to make predictions or infer trends about the larger population.

Ultimately, the goal of statistical analysis is to draw meaningful conclusions about the entire population, using data that is as comprehensive and unbiased as possible.

Data Collection

Data collection is the process of acquiring raw information for analysis. Whether collecting data from a population or a sample, the method and accuracy are pivotal to the credibility of the research.

In the exercise scenario, the data collected came from animals put on a new diet, with measurements taken over three months. To determine if this collection represents a sample or population, one must consider whether all animals on the diet were studied.

There are various ways to collect data:

• Surveys and Questionnaires: Useful for collecting qualitative data from large groups quickly.
• Experiments: Allow researchers to control and manipulate variables to gather quantitative data.
• Observations: Involve watching subjects in their natural setting to gather data without interference.

Each method has its own strengths and limitations and often, a combination of methods is used to ensure a robust dataset.

Subsets in Research

Research often involves dealing with subsets, which are smaller groups extracted from a larger population. Understanding these subsets is crucial for interpreting research outcomes. For example, the exercise discusses using twenty animals to study weight gain on a new diet, where these animals form the subset.

Identifying subsets is essential:

• They can provide insights into broader trends within the larger group.
• When representative, subsets can help researchers make informed predictions about the entire population.
• A well-chosen subset can save time and resources compared to studying an entire population.

However, careful consideration is needed to ensure subsets are unbiased and accurately reflect the larger group. This enables researchers to generalize findings more confidently.