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### Sampling Distributions

<span style="color: #91204D;"> .large[Kelly McConville | Math 141 | Week 6 | Fall 2020] </span>

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## Announcements/Reminders

* Exam next week.
    + No Week 7 labs (Th, Oct 15h or Fri, Oct 16th).
    + No Class on Fri, October 16th.
    + [Sign up for your 10 minute oral exam](https://docs.google.com/spreadsheets/d/18abmsFaa1JhwLZUbqgKZ0y7gOBH1M8brLln_TjyOspo/edit?usp=sharing)
    + You must do the 2 hour takehome exam BEFORE your oral exam!

* Lab 6 will definitely help with studying for the exam!

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## Week 6 Topics

* Modeling

* **Sampling Distributions**

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## Goals for Today

* Finish up modeling

* Discuss the ❤️ of statistical inference

* Create a Sampling Distribution

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#### The ❤️ of statistical inference is quantifying uncertainty

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### Statistical Inference

**Goal**: Draw Conclusions about the population based on the sample.

**Main Flavors**

&rarr; Estimating numerical quantities (parameters).

&rarr; Testing Conjectures

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### Estimation

**Goal**: Estimate a (population) parameter.

Best guess?

&rarr; The corresponding (sample) statistic

**Example**: Are GIFs just another way for people to share videos of their cats?

Want to estimate the proportion of GIFs that feature animals.

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### Estimation

**Key Question**: How accurate is the statistic as an estimate of the parameter?

**Helpful Sub-Question**: If we take many samples, how much would the statistic vary from sample to sample?

Need two new concepts:

* The **sampling variability** of a statistic

* The **sampling distribution** of a statistic

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### Let's learn about these ideas through an activity!