**What are population parameters?**
Population parameters are *numbers that describe a characteristic of an entire population.*
**What are the two of the most common population parameters?**
Two of the most common population parameters are:
1. Population mean - The mean value of some variable in a population.
2. Population proportion - The proportion of some variable in a population.
**What do we do if it's too costly and time-consuming to collect data from every object in a population in order to estimate a population parameter?**
If it's too costly and time-consuming to collect data from every object in a population in order to estimate a population parameter, we *take a random sample and use data from the sample to estimate the population parameter.*
**What is the point estimate?**
The point estimate is *the number that we use from the sample to estimate the population parameter.*
**What population parameters and point estimates are used with what measurements?**
The population parameters and point estimates, and the measurements they're used with, include:
| Measurement | Population Parameter | Point Estimate |
| ----------- | ----------------------------- | --------------------------- |
| Mean | $\mu$ (Population mean) | $\overline x$ (Sample mean) |
| Proportion | $\pi$ (Population proportion) | $p$ (Sample proportion) |
> [!example] Example of a situation where you'd want to use a random sample to estimate the true population mean
> Suppose we want to estimate the mean weight of a certain species of turtle in Florida. Since there are thousands of turtles in Florida, it would be extremely costly and time-consuming to go around and weigh each individual turtle. Instead, we might take a simple random sample of 50 turtles and use the mean weight of the turtles in the sample to estimate the true population mean.
> 
# The Importance Of Representative Samples
**What does an ideal sample look like?**
An ideal sample looks like *a mini version of our population.*
**When is a sample representative of a population?**
A sample is representative of a population *when the characteristics of the individuals in the sample closely match the characteristics of the individuals in the overall population.*
**What two things can you do with a representative sample of a population?**
With a representative sample of a population, two things you can do are:
1. Generalize the findings from the sample to the overall population with confidence.
2. Say that the point estimate from the sample is an unbiased estimate of the true population parameter.
# Point Estimates & Confidence Intervals
**What is true despite the point estimate of a representative sample being the best possible estimate of a true population parameter?**
Despite the point estimate of a representative sample being the best possible estimate of a true population parameter, it's true that *it's unlikely to exactly match the population parameter.*
> [!example] Example of how a point estimate from a representative sample could still not exactly match the population parameter
> The mean weight of a sample of turtles is not guaranteed to exactly match the mean weight of turtles in the whole population. For example, we might just happen to pick a sample full of low-weight turtles or perhaps a sample full of heavy turtles.
**What is created to capture the uncertainty of a point estimate from a sample?**
To capture the uncertainty of a point estimate from a sample, a *confidence interval* is created.
> **What is a confidence interval?**
> A confidence interval is *a range of values that is likely to contain a population parameter within a certain level of confidence.*
> [!example] Example of a confidence interval
> Let's say the average weight in a sample of turtles is 150.4 pounds. The confidence interval would then be range of values, perhaps from 145 pounds to 155.8 pounds.
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