📚 Topic Summary
When we're working with proportions, we often want to know if the distribution of sample proportions is approximately normal. This allows us to use powerful statistical tools. The two key conditions to check are the Random Condition and the Large Counts Condition. The random condition ensures that your sample is representative of the population. The large counts condition ensures that the sample size is big enough to produce a normal distribution.
Specifically, the Large Counts Condition states that both $np \geq 10$ and $n(1-p) \geq 10$ must be met, where $n$ is the sample size and $p$ is the population proportion. If both these conditions, along with the random condition, are satisfied, we can assume that the sampling distribution of the sample proportion is approximately normal.
🧮 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Population Proportion |
A. The size of the group being tested. |
| 2. Sample Proportion |
B. A subset of the population used for analysis. |
| 3. Sample Size |
C. The proportion of successes in a sample. |
| 4. Random Sample |
D. The proportion of successes in the entire population. |
| 5. Sample |
E. A sample where each member of the population has an equal chance of being selected. |
✍️ Part B: Fill in the Blanks
The two main conditions for a normal sampling distribution of proportions are the ______ condition and the ______ Counts condition. The ______ condition helps ensure that the sample represents the ______ . The Large Counts condition states that $np \geq 10$ and $n(1-p) \geq ______$ must both be satisfied.
🤔 Part C: Critical Thinking
Explain in your own words why it's important to check the conditions for a normal sampling distribution of proportions before conducting statistical inference.