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Understanding Data Collection Methods and Bias in Statistics
Published on April 10, 2026
Statistics
Analyze the accuracy of different data collection methods, including surveys and observational studies, to determine the most reliable approach for representing a population.
Question
Answer
Here’s a step-by-step analysis of each statement:
Statement (a): “A survey about parenting styles given to every tenth student entering the library will provide unbiased results.”
This statement describes a systematic sampling method. However, the population of students entering the library might not be representative of all students in the school, as students who use the library might have different parenting styles than those who don’t. Therefore, this method could introduce bias.
This statement describes a systematic sampling method. However, the population of students entering the library might not be representative of all students in the school, as students who use the library might have different parenting styles than those who don’t. Therefore, this method could introduce bias.
Statement (b): “An observational study allows a researcher to determine the cause of an outcome.”
Observational studies observe subjects and measure variables of interest without assigning treatments or interventions. While they can identify associations and correlations between variables, they generally cannot establish causation. This is because confounding variables might be present, making it impossible to isolate the effect of one variable on another. To determine cause and effect, controlled experiments are usually required.
Observational studies observe subjects and measure variables of interest without assigning treatments or interventions. While they can identify associations and correlations between variables, they generally cannot establish causation. This is because confounding variables might be present, making it impossible to isolate the effect of one variable on another. To determine cause and effect, controlled experiments are usually required.
Statement ©: “Margin of error increases as sample size increases.”
The margin of error is a statistical measure of the amount of random sampling error in a survey’s results. The margin of error is inversely related to the sample size. As the sample size increases, the margin of error decreases, meaning the results are more precise and closer to the true population value. Conversely, as the sample size decreases, the margin of error increases.
The margin of error is a statistical measure of the amount of random sampling error in a survey’s results. The margin of error is inversely related to the sample size. As the sample size increases, the margin of error decreases, meaning the results are more precise and closer to the true population value. Conversely, as the sample size decreases, the margin of error increases.
Statement (d): “A survey collected from a random sample of students in a school can be used to represent the opinions of the school population.”
This statement describes a fundamental principle of statistical inference. When a sample is selected randomly from a population, it is likely to be representative of that population. This allows researchers to generalize the findings from the sample to the larger population with a certain degree of confidence.
This statement describes a fundamental principle of statistical inference. When a sample is selected randomly from a population, it is likely to be representative of that population. This allows researchers to generalize the findings from the sample to the larger population with a certain degree of confidence.
Comparing the statements, statement (d) is the most accurate and fundamental principle of data collection for making inferences about a population.
The final answer is