Standard Error
Definition
The standard error is a measure of the variability or spread of sample means around the population mean. It tells us how much we can expect sample means to differ from the true population mean.
Analogy
Imagine you have a group of friends who are all trying to estimate the average height of people in your school. Each friend randomly selects a few students and measures their heights. The standard error would be like the range of heights that each friend gets, showing how much their estimates vary from each other and from the actual average height.
Related terms
Confidence Interval: A confidence interval is a range of values that likely contains the true population parameter with a certain level of confidence.
Sampling Distribution: A sampling distribution is a theoretical distribution that shows all possible sample statistics for a given sample size taken from a population.
Margin of Error: The margin of error is an interval around an estimated value that accounts for uncertainty due to sampling variability. It indicates how close our estimate might be to the true population parameter.
"Standard Error" appears in:
Study guides (7)
AP Statistics - 6.7 Potential Errors When Performing Tests
AP Statistics - 6.8 Confidence Intervals for the Difference of Two Proportions
AP Statistics - 7.2 Constructing a Confidence Interval for a Population Mean
AP Statistics - 7.3 Justifying a Claim About a Population Mean Based on a Confidence Interval
AP Statistics - 7.7 Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
AP Statistics - 7.9 Carrying Out a Test for the Difference of Two Population Means
AP Statistics - 9.3 Justifying a Claim About the Slope of a Regression Model Based on a Confidence Interval
Practice Questions (5)
- How does the width of a confidence interval change as the standard error of the slope decreases?
- What is the relationship between the standard error of the slope and the precision of the estimate?
- How is the standard error calculated?
- What happens to the standard error as the sample size increases?
- Which of the following of the sampling distribution of the sample mean is also called the standard error of the mean?
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