27. Quiz + Text: Recap & Next Steps

QUIZ QUESTION: :

Recap Quiz

Match each term to the correct definition to assure you mastered the concepts in this lesson.

ANSWER CHOICES:

A numeric summary of a sample.

A numeric summary of a population.

The distribution of a statistic.

Used to notate parameters.

Sampling with replacement.

Definition	Term
parameter
Greek symbols
sampling distribution
bootstrapping
statistic

SOLUTION:

Definition	Term
parameter	A numeric summary of a population.
Greek symbols	Used to notate parameters.
sampling distribution	The distribution of a statistic.
bootstrapping	Sampling with replacement.
statistic	A numeric summary of a sample.

QUIZ QUESTION: :

Recap Quiz 2

Match each term to the correct definition to assure you mastered the concepts in this lesson.

ANSWER CHOICES:

A theorem that states: the larger the sample size, the closer our statistic gets to the parameter.

A theorem that states: if our sample size is large enough, the sample mean will be normally distributed.

Describing the data we have collected.

Using the data we have collected to draw conclusions about our population of interest.

Definition	Term
The Central Limit Theorem
Descriptive Statistics
Law of Large Numbers
Inferential Statistics

SOLUTION:

Definition	Term
The Central Limit Theorem	A theorem that states: if our sample size is large enough, the sample mean will be normally distributed.
Descriptive Statistics	Describing the data we have collected.
Law of Large Numbers	A theorem that states: the larger the sample size, the closer our statistic gets to the parameter.
Inferential Statistics	Using the data we have collected to draw conclusions about our population of interest.

Recap

In this lesson, you have learned a ton! You learned:

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Sampling Distributions

• Sampling Distributions are the distribution of a statistic (any statistic).
  
  
• There are two very important mathematical theorems that are related to sampling distributions: The Law of Large Numbers and The Central Limit Theorem .
  
  
• The Law of Large Numbers states that as a sample size increases, the sample mean will get closer to the population mean. In general, if our statistic is a "good" estimate of a parameter, it will approach our parameter with larger sample sizes.
  
  
• The Central Limit Theorem states that with large enough sample sizes our sample mean will follow a normal distribution, but it turns out this is true for more than just the sample mean.

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Bootstrapping

• Bootstrapping is a technique where we sample from a group with replacement.
  
  
• We can use bootstrapping to simulate the creation of sampling distribution, which you did many times in this lesson.
  
  
• By bootstrapping and then calculating repeated values of our statistics, we can gain an understanding of the sampling distribution of our statistics.

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Looking Ahead

In this lesson you gained the fundamental ideas that will help you with the next two lessons by learning about sampling distributions and bootstrapping. These are going provide the basis for confidence intervals and hypothesis testing in the next two lessons.