minor typo updates and updated PDFs to be posted

OpenIntroStat · Jul 7, 2016 · 3c58b87 · 3c58b87
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diff --git a/01/01learn_obj.log b/01/01learn_obj.log
@@ -1,4 +1,4 @@
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diff --git a/01/01learn_obj.pdf b/01/01learn_obj.pdf
diff --git a/01/01learn_obj.synctex.gz b/01/01learn_obj.synctex.gz
diff --git a/01/01learn_obj.tex b/01/01learn_obj.tex
@@ -81,7 +81,7 @@
 \item If random assignment has been employed in study design, the results suggest causality.
 \end{itemize}
 \item Question confounding variables and sources of bias in a given study.
-\item Distinguish between simple random, stratified, and cluster sampling, and recognize the benefits and drawbacks of choosing one sampling scheme over another.
+\item Distinguish between simple random, stratified, cluster, and multistage sampling, and recognize the benefits and drawbacks of choosing one sampling scheme over another.
 \begin{itemize}
 \renewcommand{\labelitemi}{{\textcolor{dark}{{\tiny $\blacksquare$}}}}
 \item Simple random sampling: Each subject in the population is equally likely to be selected.

diff --git a/02/02learn_obj.log b/02/02learn_obj.log
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diff --git a/02/02learn_obj.pdf b/02/02learn_obj.pdf
diff --git a/02/02learn_obj.synctex.gz b/02/02learn_obj.synctex.gz
diff --git a/02/02learn_obj.tex b/02/02learn_obj.tex
@@ -57,26 +57,26 @@
 \item Define a probability distribution as a list of the possible outcomes with corresponding probabilities that satisfies three rules: 
 \begin{itemize}
 \item[-] The outcomes listed must be disjoint. 
-\item[-] Each probability must be between 0 and 1.
+\item[-] Each probability must be between 0 and 1, inclusive.
 \item[-] The probabilities must total 1. 
 \end{itemize}
 
 \item Define complementary outcomes as mutually exclusive outcomes of the same random process whose probabilities add up to 1. 
 \begin{itemize}
-\item[-] If A and B are complementary, P(A) + P(B) = 1 
+\item[-] If A and B are complementary, $P(A) + P(B) = 1$.
 \end{itemize}
 
 \item Distinguish between union of events (A or B) and intersection of events (A and B).
 \begin{itemize}
 \item[-] Calculate the probability of union of events using the (general) addition rule.
 \begin{itemize}
-\item[+] If A and B are not mutually exclusive, P(A or B) = P(A) + P(B) ? P(A and B) 
-\item[+] If A and B are mutually exclusive, P (A or B) = P (A) + P (B), since for mutually exclusive events P(A and B) = 0 
+\item[+] If A and B are not mutually exclusive, $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$.
+\item[+] If A and B are mutually exclusive, $P(A \text{ or } B) = P (A) + P (B)$, since for mutually exclusive events $P(A \text{ and } B) = 0$.
 \end{itemize}
 \item[-] Calculate the probability of intersection of independent events using the multiplication rule.
 \begin{itemize}
-\item[+] If A and B are independent, P(A and B) = P(A) ? P(B) 
-\item[+] If A and B are dependent, P(A and B) = P(A|B) ? P(B) 
+\item[+] If A and B are dependent, $P(A \text{ and } B) = P(A) \times P(B | A)$.
+\item[+] If A and B are dependent, independent, $P(A \text{ and } B) = P(A) \times P(B)$,  since for independent events $P(B | A) = P(B)$.
 \end{itemize}
 \end{itemize}
 

diff --git a/04/04learn_obj.log b/04/04learn_obj.log
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diff --git a/04/04learn_obj.pdf b/04/04learn_obj.pdf
diff --git a/04/04learn_obj.synctex.gz b/04/04learn_obj.synctex.gz
diff --git a/04/04learn_obj.tex b/04/04learn_obj.tex
@@ -315,7 +315,7 @@
 \item Reading: Section 4.5 of OpenIntro Statistics
 \item Test yourself: \\
 {\small
-In a random sample of 1,017 Americans 60\% said they do not trust the mass media when it comes to reporting the news fully, accurately, and fairly. The standard error associated with this estimate is 0.015 (1.5\%). What is the margin of error ay 95\% confidence level? Calculate a 95\% confidence interval and interpret it in context. You may assume that the point estimate is normally distributed (we'll learn how to check this later).
+In a random sample of 1,017 Americans 60\% said they do not trust the mass media when it comes to reporting the news fully, accurately, and fairly. The standard error associated with this estimate is 0.015 (1.5\%). What is the margin of error for a 95\% confidence level? Calculate a 95\% confidence interval and interpret it in context. You may assume that the point estimate is normally distributed (we'll learn how to check this later).
 }
 \end{itemize}
 }}

diff --git a/05/05learn_obj.tex b/05/05learn_obj.tex
@@ -38,7 +38,7 @@
 
 \begin{document}
 
-{\LARGE \textcolor{oiB}{Learning Objectives \hfill Chapter 5: Inference for numerical variables}} \\
+{\LARGE \textcolor{oiB}{Learning Objectives \hfill Chapter 5: Inference for numerical data}} \\
 
 %
 

diff --git a/06/06learn_obj.log b/06/06learn_obj.log
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diff --git a/06/06learn_obj.pdf b/06/06learn_obj.pdf
diff --git a/06/06learn_obj.synctex.gz b/06/06learn_obj.synctex.gz
diff --git a/06/06learn_obj.tex b/06/06learn_obj.tex
@@ -38,7 +38,7 @@
 
 \begin{document}
 
-{\LARGE \textcolor{oiB}{Learning Objectives \hfill Chapter 6: Inference for categorical variables}} \\
+{\LARGE \textcolor{oiB}{Learning Objectives \hfill Chapter 6: Inference for categorical data}} \\
 
 %
 \begin{enumerate}
@@ -71,14 +71,14 @@
 
 \item Note that the standard error calculation for the confidence interval and the hypothesis test are different when dealing with proportions, since in the hypothesis test we need to assume that the null hypothesis is true -- remember: p-value = P(observed or more extreme test statistic $|$ $H_0$ true).
 \begin{itemize}
-\item[-] For confidence intervals use $\hat{p}$ (observed sample proportion) when calculating the standard error and checking the success/failure condition:
+\item[-] For confidence intervals use $\hat{p}$ (observed sample proportion) when calculating the standard error and when checking the success/failure condition:
 \[ SE_{\hat{p}} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]
 \item[-] For hypothesis tests use $p_0$ (null value) when calculating the standard error and checking the success/failure condition:
 \[ SE_{\hat{p}} = \sqrt{\frac{p_0 (1-p_0)}{n}} \]
 \item[-] Such a discrepancy doesn't exist when conducting inference for means, since the mean doesn't factor into the calculation of the standard error, while the proportion does.
 \end{itemize}
 
-\item Explain why when calculating the required minimum sample size for a given margin of error at a given confidence level, we use $\hat{p} = 0.5$ if there are no previous studies suggesting a more accurate estimate.
+\item Calculate the required minimum sample size for a given margin of error at a given confidence level, and explain why we use $\hat{p} = 0.5$ if there are no previous studies suggesting a more accurate estimate.
 \begin{itemize}
 \item[-] Conceptually: When there is no additional information, 50\% chance of success is a good guess for events with only two outcomes (success or failure).
 \item[-] Mathematically: Using $\hat{p} = 0.5$ yields the most conservative (highest) estimate for the required sample size.
@@ -117,7 +117,7 @@
 
 \item Note that the calculation of the standard error of the distribution of the difference in two independent sample proportions is different for a confidence interval and a hypothesis test.
 \begin{itemize}
-\item[-] confidence interval and hypothesis test when $H_0: p_1 -p_2 =$ some value other than 0: 
+\item[-] confidence interval (and hypothesis test when $H_0: p_1 -p_2 =$ some value other than 0): 
 \[SE_{(\hat{p}_1 - \hat{p}_2)} = \sqrt{\frac{ \hat{p}_1 (1 - \hat{p}_1)}{n_1} + \frac{ \hat{p}_2 (1 - \hat{p}_2)}{n_2} } \]
 \item[-] hypothesis test when $H_0: p_1 -p_2 = 0$: 
 \[SE_{(\hat{p}_1 - \hat{p}_2)} = \sqrt{\frac{ \hat{p}_{pool} (1 - \hat{p}_{pool})}{n_1} + \frac{ \hat{p}_{pool} (1 - \hat{p}_{pool})}{n_2} }, \]
@@ -166,8 +166,8 @@
 
 \item Use a chi-square test of goodness of fit to evaluate if the distribution of levels of a single categorical variable follows a hypothesized distribution.
 \begin{itemize}
-\item[] $H_0:$ The distribution of observed counts follow the hypothesized distribution, and any observed differences are due to chance.
-\item[] $H_A:$ The distribution of observed counts do not follow the hypothesized distribution.
+\item[] $H_0:$ The distribution of the variable follows the hypothesized distribution, and any observed differences are due to chance.
+\item[] $H_A:$ The distribution of the variable does not follow the hypothesized distribution.
 \end{itemize}
 
 \item Calculate the expected counts for a given level (cell) in a one-way table as the sample size times the hypothesized proportion for that level.
@@ -176,7 +176,7 @@
 \[ \chi = \sum_{i = 1}^{k}  \frac{(\text{observed count} - \text{expected count})^2}{\text{expected count}}, \]
 where $k$ is the number of cells.
 
-\item Note that the chi-square distribution is right skewed with one parameter: degrees of freedom. In the case of a goodness of fit test, $df = k - 1$.
+\item Note that the chi-square distribution is right skewed with one parameter: degrees of freedom. In the case of a goodness of fit test, $df = \# \text{of categories} - 1$.
 
 \item List the conditions necessary for performing a chi-square test (goodness of fit or independence)
 \begin{enumerate}

diff --git a/07/07learn_obj.log b/07/07learn_obj.log
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diff --git a/07/07learn_obj.pdf b/07/07learn_obj.pdf
diff --git a/07/07learn_obj.synctex.gz b/07/07learn_obj.synctex.gz
diff --git a/07/07learn_obj.tex b/07/07learn_obj.tex
@@ -65,11 +65,11 @@
 \item[-] Note that a relationship that is nonlinear is simply called an association.
 \end{itemize}
 
-\item Note that correlation coefficient ($R$, also called Pearson's $R$) the following properties:
+\item Note that correlation coefficient ($r$, also called Pearson's $r$) the following properties:
 \begin{enumerate}
 \item[-] the magnitude (absolute value) of the correlation coefficient measures the strength of the linear association between two numerical variables
 \item[-] the sign of the correlation coefficient indicates the direction of association
-\item[-] the correlation coefficient is always between -1 and 1, -1 indicating perfect negative linear association, +1 indicating perfect positive linear association, and 0 indicating no linear relationship
+\item[-] the correlation coefficient is always between -1 and 1, inclusive, with -1 indicating perfect negative linear association, +1 indicating perfect positive linear association, and 0 indicating no \emph{linear} relationship
 \item[-] the correlation coefficient is unitless
 \item[-] since the correlation coefficient is unitless, it is not affected by changes in the center or scale of either variable (such as unit conversions)
 \item[-] the correlation of X with Y is the same as of Y with X 
@@ -126,7 +126,7 @@
 
 \item Calculate the estimate for the slope ($b_1$) as 
 \[ b_1 = R\frac{s_y}{s_x}, \]
-where $R$ is the correlation coefficient, $s_y$ is the standard deviation of the response variable, and $s_x$ is the standard deviation of the explanatory variable.
+where $r$ is the correlation coefficient, $s_y$ is the standard deviation of the response variable, and $s_x$ is the standard deviation of the explanatory variable.
 
 \item Interpret the slope as 
 \begin{itemize}
@@ -157,7 +157,7 @@
 \item Define $R^2$ as the percentage of the variability in the response variable explained by the the explanatory variable.
 \begin{itemize}
 \item[-] For a good model, we would like this number to be as close to 100\% as possible.
-\item[-] This value is calculated as the square of the correlation coefficient.
+\item[-] This value is calculated as the square of the correlation coefficient, and is between 0 and 1, inclusive.
 \end{itemize}
 
 \end{enumerate}

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