📚 Topic Summary
When we want to understand something about a large group (called a population), we often take a smaller group (called a sample) and study that. A sampling distribution shows how sample statistics (like the average) vary from sample to sample. This activity explores how the sample size affects the shape of that distribution. Larger samples generally give us a sampling distribution that is more like the true population and more closely approximates a normal distribution. As the sample size increases, the standard deviation of the sampling distribution decreases and the data in the sampling distribution becomes more concentrated near the mean of the sampling distribution.
🧪 Part A: Vocabulary
Match the terms to their definitions:
| Term |
Definition |
| 1. Sample Size |
A. A characteristic or measure obtained by using all the data values from a population. |
| 2. Sampling Distribution |
B. The set of all possible values of a statistic computed from repeated random samples of the same size from a population. |
| 3. Population Parameter |
C. The entire group of individuals that is the target of our interest. |
| 4. Population |
D. The number of observations in a sample. |
| 5. Sample Statistic |
E. A characteristic or measure obtained by using the data values from a sample. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: larger, smaller, normal, mean.
As the sample size becomes ____, the sampling distribution tends to become more ____. This means that with ____ samples, our estimate is likely to be closer to the true ____.
🤔 Part C: Critical Thinking
Explain, in your own words, why a larger sample size generally leads to a more accurate estimate of the population parameter. Think about real-world examples!