Sampling Distribution
Definition
A sampling distribution refers to the distribution of a statistic (such as mean, proportion, or difference) calculated from multiple random samples taken from the same population. It provides information about how sample statistics vary from sample to sample.
Analogy
Think of a sampling distribution as a collection of different-sized ice cream scoops taken from a giant tub of ice cream. Each scoop represents a random sample, and by examining all these scoops together, you can get an idea of how consistent or variable the amount of ice cream in each scoop is.
Related terms
Central Limit Theorem: The central limit theorem states that for large enough sample sizes, regardless of the shape of the population distribution, the sampling distribution of the mean will be approximately normal.
Standard Error: The standard error measures how much variability there is in sample statistics across different samples. It quantifies how close or far off these statistics are likely to be from their true population values.
Confidence Interval: A confidence interval is an interval estimate that provides a range within which we are confident that a population parameter (e.g., mean or proportion) lies based on our sample data.
"Sampling Distribution" appears in:
Study guides (7)
AP Statistics - 5.1 Introducing Statistics: Why Is My Sample Not Like Yours?
AP Statistics - 5.4 Biased and Unbiased Point Estimates
AP Statistics - 5.6 Sampling Distributions for Differences in Sample Proportions
AP Statistics - 5.7 Sampling Distributions for Sample Means
AP Statistics - 6.2 Constructing a Confidence Interval for a Population Proportion
AP Statistics - 6.3 Justifying a Claim Based on a Confidence Interval for a Population Proportion
AP Statistics - 6.11 Carrying Out a Test for the Difference of Two Population Proportions
Additional resources (5)
Practice Questions (20+)
- What happens to the spread of a sampling distribution as the sample size increases?
- What condition must be satisfied in order for us to assume that the sampling distribution of the sample proportion is approximately normal?
- In the context of sample proportions, what does the sampling distribution represent?
- If the true population proportion is 0.3, what is the center of the sampling distribution for the sample proportion?
- If the true population proportion is 0.76 and the sizes of the samples taken from the population are 50, what can be said about the shape of the sampling distribution for the sample proportion?
- If the sample size is 500 and the true population proportion is 0.42, what is the standard deviation of the sampling distribution for the sample proportion?
- If the population proportion is 0.3 and the samples taken from the population are of size 40, what can be said about the shape of the sampling distribution for the sample proportion?
- If the sample drawn from the population is of size 100 and the true population proportion is 0.38, what is the standard deviation of the sampling distribution for the sample proportion?
- If the mean of the sampling distribution for the sample proportion is 0.59, what is the true population proportion?
- What does the sampling distribution for the difference in sample proportions represent?
- What are the right conditions to determine that a sample distribution are roughly normal for the sampling distribution of the difference in sample proportions?
- What is the center of the sampling distribution(B - A) for the difference in sample proportions if the true population proportions of City A and City B are 0.6 and 0.7?
- In a sampling distribution for differences in sample proportions, what will happen to the standard deviation if the sample sizes are increased?
- What does the sampling distribution for a sample mean represent?
- Why is the sampling distribution for the sample mean useful?
- In which scenario can you use the sampling distribution of the sample mean to model using a normal distribution?
- If a sample of size 50 is taken from a population with a known mean and standard deviation, how would you describe the shape of the sampling distribution of the sample mean?
- What is the center of the sampling distribution for the sample mean when the true population mean is $45,000 per year?
- When can the sampling distribution of a sample mean be approximated as normal, regardless of the actual population distribution?
- If the two population distributions can be modeled with a normal distribution, what can be inferred about the sampling distribution of the difference in sample means?
Resources
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