## Quiz 1 Review

• General remarks

• read the questions carefully, especially the bold and underlined parts.
• The full solutions are on ICON.
• Section A01

• 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 & p-values?

• Testing a hypothesis: clothing is the first choice for most adults, so we need to find a a test statistic ($$Z$$) and a p-value. CI and hypothesis tests are related, but a p-value 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?
• 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 p-value 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 p-value on p. 26. We reject $$H_0$$ when the p-value (the risk of wrongly rejection $$H_0$$ when it's actually true) is small compared the $$\alpha$$, our risk tolerance.

## 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 & p-values?

• Testing a hypothesis: clothing is the first choice for most adults, so we need to find a a test statistic ($$Z$$) and a p-value. CI and hypothesis tests are related, but a p-value 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?
• When to reject vs. fail to reject $$H_0$$?

• Look at the definitions of a p-value on p. 26. We reject $$H_0$$ when the p-value (the risk of wrongly rejection $$H_0$$ when it's actually true) is small compared the $$\alpha$$, our risk tolerance.
• $$p_0$$ 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.