What Is A Point Estimate by Zach Bobbitt

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 (Population mean) (Sample mean)
Proportion (Population proportion) (Sample proportion)
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 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 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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