Margin of Error

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What is the definition of Margin of Error?

Back

The Margin of Error is a statistic that expresses the amount of random sampling error in a survey's results. It indicates the range within which the true population parameter is expected to fall.

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How is the sample proportion calculated?

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The sample proportion is calculated by dividing the number of successes (e.g., people who own a dog) by the total number of observations in the sample.

Front

If a survey shows that 80 out of 200 people own a dog, what is the sample proportion?

Back

0.4

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What does a Margin of Error of 2% indicate in survey results?

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It indicates that the true population parameter is likely to fall within 2 percentage points above or below the reported statistic.

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What is the formula for calculating the Margin of Error?

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Margin of Error = Z * (σ/√n), where Z is the Z-score corresponding to the confidence level, σ is the standard deviation, and n is the sample size.

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What is a confidence interval?

Back

A confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter.

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In a survey of 2000 high schoolers, if 80% use their phones more than 4 hours a day, what is the expected interval for the population?

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78% - 82%.

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Why is a larger sample size preferred in surveys?

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A larger sample size reduces the Margin of Error, leading to more reliable and accurate results.

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What is the difference between a sample and a population?

Back

A sample is a subset of individuals selected from a larger group (population) used to estimate characteristics of the whole population.

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What is a parameter in statistics?

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A parameter is a numerical value that summarizes a characteristic of a population, such as the population mean or proportion.