Population Mean
Definition
The population mean is the average value of a variable for an entire population. It represents a summary measure for all individuals or units within that population.
Analogy
Think of your school as a whole population, and imagine calculating the average height of all students combined. The population mean would represent this overall average height, taking into account every student's measurement.
Related terms
Sampling Distribution: A sampling distribution shows all possible values for an estimator (such as sample mean) when repeated samples are taken from a population. The mean value from this distribution corresponds to the population mean.
Parameter Estimation: Parameter estimation involves using sample data to make educated guesses about unknown population parameters. The population mean is often a parameter of interest for estimation.
Central Limit Theorem: The central limit theorem states that, under certain conditions, the sampling distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This theorem is essential for estimating population means.
"Population Mean" appears in:
Study guides (6)
AP Statistics - 5.7 Sampling Distributions for Sample Means
AP Statistics - 5.8 Sampling Distributions for Differences in Sample Means
AP Statistics - 7.3 Justifying a Claim About a Population Mean Based on a Confidence Interval
AP Statistics - 7.4 Setting Up a Test for a Population Mean
AP Statistics - 8.1 Introducing Statistics: Are My Results Unexpected?
AP Statistics - 9.2 Confidence Intervals for the Slope of a Regression Model
Additional resources (1)
Practice Questions (20+)
- In constructing a confidence interval for a population mean, increasing the confidence level from 90% to 95% will result in:
- In constructing a confidence interval for a population mean, increasing the confidence level will result in:
- A researcher wants to construct a 95% confidence interval for the population mean. Which of the following z-scores should be used?
- When constructing a confidence interval for a population mean, increasing the sample size will result in:
- In constructing a confidence interval for a population mean when the population standard deviation is unknown and the sample size is small, which distribution should be used?
- What is the margin of error in a confidence interval for a population mean?
- In constructing a confidence interval for a population mean, a higher level of confidence will result in:
- Which of the following is NOT required when constructing a confidence interval for a population mean?
- When constructing a confidence interval for a population mean, increasing the sample size will have what effect on the margin of error?
- A researcher wants to construct a 99% confidence interval for a population mean. Which of the following z-scores should be used?
- When constructing a confidence interval for a population mean, a larger standard deviation would result in:
- What is the formula used to construct a confidence interval for a population mean when the population standard deviation is known?
- The confidence interval for a population mean provides an estimate of:
- What is a statistical claim for the population mean?
- What is the recommended minimum sample size when testing a statistical claim about a population mean?
- What does it indicate if the confidence interval for a population mean becomes thinner?
- What is the recommended confidence level for constructing a confidence interval for a population mean?
- What is the purpose of conducting additional studies or gathering more data when the claimed population mean falls outside of the confidence interval?
- When performing a significance test for a population mean, what is the test statistic used?
- What information should be included in a written response for a t-test for population mean?
Resources
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