Inference: Sample Size

Sample size is crucial for making informed decisions based on data collected.
More information leads to better decisions, providing greater knowledge.
However, there's a trade-off in selecting the optimal sample size.
- Small Sample Size: Pros: Quick data collection. Cons: Limited data leads to lower precision.
- Large Sample Size: Pros: More precise and reliable data. Cons: Time-consuming data collection.
The goal is to find a balance: sufficient data without excessive collection time.
**Sampling Methods: **
- Simple Random Sampling: All individuals have an equal chance of being selected.
- Stratified Sampling: The population is divided into subgroups, and samples are drawn from these groups.

Definition: A method where every individual in the population is chosen at random.
Example: In a class of 30 students, selecting 6 students randomly constitutes a sample size of 6.

Example Scenario: Investigating travel times between bus riders and walkers among students.
Conducting a simple random sample of 100 students is sufficient for the investigation.
For merit: Description of the sampling process and method must be included, specifying the randomness of selection.

Definition: Starts with the whole population and divides it into groups (strata) before sampling.
Example: Split population into females and males, then take random samples within each group.
Sample Size Reporting: Specify sample sizes for each subgroup.
- Example: 4 females and 4 males, chosen randomly within their respective groups.
Further Example: To compare travel times, take 100 samples from bus riders and 100 from walkers, ensuring stratified methods are used.

Additional Scenario: Group high school students into those who catch the bus vs. those who walk.
Take a sample size of 100 from each group to adequately represent both categories for analysis.