
General remarks
 read the questions carefully, especially the bold and underlined parts.
 The full solutions are on ICON.
 Section B42
Section A01
#1
 Don't mix up the sample statistic with the sample. The sample is a group of some objects (bars, people, etc.). The statistic is some number that describes the sample (the proportion checking IDs).
 The actual number of bars checking IDs isn't that interesting, since it depends on the size of the sample or population. If I just say 3 bars didn't check IDs, is that meaningful? You need to know how many bars I visited to put those 3 that didn't check IDs in context.
#2

Means vs. proportions problem:
 What kind of data do you have? Is it categorical (proportions) or quantitative (means)?
 Use the \(t\) table for means and the \(Z\) for proportions. Step 1 includes defining the parameter or parameters. In this case that means \(p\): the proportion of all adults who choose clothing first.

When to use CI vs. test statistic & pvalues?
 Testing a hypothesis:
clothing is the first choice for most adults
, so we need to find a a test statistic (\(Z\)) and a pvalue. CI and hypothesis tests are related, but a pvalue is exactly what we need for the hypothesis tests: What is the probability of wrongly rejecting \(H_0\) based on our sample when \(H_0\) is actually true?
 Testing a hypothesis:

A lot of people did hypothesis tests on the statistic instead of the parameter (i.e. \(H_A: \hat{p} > 0.5\)). But we already know \(\hat{p} = .47719 < .5\), so there's no reason to do a hypothesis test on that. We don't know the value of the parameter \(p\), so we do the hypothesis test on it.

Shading helps. In this case we had
\begin{align}
H_A &= p > 0.5 \\\\
H_0 &= p \leq 0.5
\end{align}
The pvalue is evidence for \(H_A\), so we want to shade to the right.
 When to reject vs. fail to reject \(H_0\)?
 Look at the definitions of a pvalue on
p. 26
. We reject \(H_0\) when the pvalue (the risk of wrongly rejection \(H_0\) when it's actually true) is small compared the \(\alpha\), our risk tolerance.
 Look at the definitions of a pvalue on
Section B42
#1
 Don't mix up the population parameter with the population. The population is a set of objects (people, bars, etc). and the parameter is a number (probably unknown) that describes them.
#2
 Make sure to define the parameter or parameters.

When to use CI vs. test statistic & pvalues?
 Testing a hypothesis:
clothing is the first choice for most adults
, so we need to find a a test statistic (\(Z\)) and a pvalue. CI and hypothesis tests are related, but a pvalue is exactly what we need for the hypothesis tests: What is the probability of wrongly rejecting \(H_0\) based on our sample when \(H_0\) is actually true?
 Testing a hypothesis:

When to reject vs. fail to reject \(H_0\)?
 Look at the definitions of a pvalue on
p. 26
. We reject \(H_0\) when the pvalue (the risk of wrongly rejection \(H_0\) when it's actually true) is small compared the \(\alpha\), our risk tolerance.
 Look at the definitions of a pvalue on
 \(p_0\) vs. \(\hat{p}\) in the denominator for \(Z\). Be careful with the formula.
It is true that clothing is the first choice ...
vs.Sufficient evidence to conclude that clothing is the first choice ...
aren't quite the same.
2b: Select \(H_a \neq\) to get a CI and check the box to use the normal (Z) distrubtion.