3.2. Learning Objectives

The learning objectives for this week are closely related to those of the previous week

3.2.1. Conceptual

After this week you should be able to:

• Define the term sample and population

• Understand the difference between sampling with and without replacement

• Define the sampling distribution of a statistic (such as the sample mean or proportion)

• Explain how the standard error depends on sample size \(n\) and the population variability \(\sigma\)

• Understand that the estimated sampling distribution of the mean for a population can be obtained in several ways including:

  • Calculated empirically from the population - draw many samples of size \(n\) from the population and plot their means

  • Modelled using a known distribution (Normal if central limit theorem applies)

This material is covered in the lecture and recapped in the worked examples in Python

3.2.2. Python skills

This week there is an emphasis on simulating the process of drawing a large number of (re)samples from a sample distribution

The key skill practiced this week is building a for loop to repeat a process many times (such as drawing a random sample and getting its mean)

You might need to change some variable (such as sample size n) on each pass through the loop.

Additional new(ish) Python skills:

• sample from a pandas dataframe using pandas.df.sample()

• Plot an expected distribution such as a curve from the function stats.norm.pdf() over a histogram of simulated data

• Plot a Q-Q plot

This material is covered in the Jupyter Notebooks in this section