

Connections
• Exploratory Data Analysis
 Like confidence intervals, hypothesis tests help students
use data to just answer that simple investigative question that they
may have developed about a particular population. This should reference
back to the first unit of the course.
 In order to evaluate whether assumptions hold, need to look
at shape, center, spread of sample distribution.
• Inference
 Like confidence intervals, hypothesis tests help us make
inference about a population using just a single sample. Just as the
previous units discussed, it is important to reiterate that we just
need one sample to make inference.
 Again like confidence intervals, hypothesis tests rely on
sampling distributions and the Central Limit Theorem (if assumptions
are met), so it is important to show students how these concepts all
relate.
 For assumptions to be met, we need to follow good data
collection practices to obtain a random sample.
 If the Central Limit Theorem applies, students will need to
recall normal models and zscores. Remember: their sample may not be
normal, but the sampling distribution of their sample mean or
proportion is normal under Central Limit Theorem.
 It is very important to draw students back to informal
inference done earlier using simulations; show them the same example
using both methods so they can see that both achieve same goal; one is
just a shortcut/approximation that might be faster to do.
 If students can understand the intuition behind
simulationbased inference, then formal hypothesis testing is just a
shortcut we can use when assumptions are met that does the same thing
with less work.
 pvalues are just how likely we are to get the observed
statistic if we assume a certain model/hypothesis is true; this is the
case whether we use the normal model (and look at a shaded region
beyond the observed value) or use a model built from many simulations
(and count the observations beyond the observed value).
• Models
 In this course, we assume sampling distribution follows a
model with some hypothesized mean.
 But no matter what, we assume some “chance” model that is
plausible for our estimate.
 It is plausible that our estimate comes from this model,
but how plausible given the mean of that model? If it’s not very
plausible, then we should look for a new model.
• Probability
 The pvalue is just a conditional probability; given the
null hypothesis, what is the probability of getting the observed
statistic (or something more extreme)?
