Merge commit '33a0fc9'

* commit '33a0fc9':
  fix typos and adjust wording in hw3, knit html with slidify

Author: rdpeng

06_StatisticalInference/homework/hw1.html

@@ -63,13 +63,13 @@ <h2>About these slides</h2>
   <article data-timings="">
 
 <div class="quiz quiz-single well ">
-  <p>Consider influenza epidemics for two parent heterosexual families. Suppose that the probability is 15% that at least one of the parents has contracted the disease. The probability that the father has contracted influenza is 6% while that the mother contracted the disease is 5%. What is the probability that both contracted influenza expressed as a whole number percentage?</p>
+  <p>Consider influenza epidemics for two parent heterosexual families. Suppose that the probability is 15% that at least one of the parents has contracted the disease. The probability that the father has contracted influenza is 10% while that the mother contracted the disease is 9%. What is the probability that both contracted influenza expressed as a whole number percentage?</p>
 
 <ol>
 <li>15%</li>
-<li>6%</li>
-<li>5%</li>
-<li><em>2%</em></li>
+<li>10%</li>
+<li>9%</li>
+<li><em>4%</em></li>
 </ol>
 
   <button class="quiz-submit btn btn-primary">Submit</button>
@@ -78,18 +78,18 @@ <h2>About these slides</h2>
   <button class="quiz-clear btn btn-danger">Clear</button>
 
   <div class="quiz-hint">
-  <p>\(A = Father\), \(P(A) = .06\), \(B = Mother\), \(P(B) = .05\) 
+  <p>\(A = Father\), \(P(A) = .10\), \(B = Mother\), \(P(B) = .09\) 
 \(P(A\cup B) = .15\), </p>
 
 </div>
 <div class="quiz-explanation">
-  <p>\(P(A\cup B) = P(A) + P(B) - 2 P(AB)\) thus
-\[.15 = .06 + .05 - 2 P(AB)\]</p>
+  <p>\(P(A\cup B) = P(A) + P(B) - P(AB)\) thus
+\[.15 = .10 + .09 - P(AB)\]</p>
 
-<pre><code class="r">(0.15 - .06 - .05) / 2
+<pre><code class="r">.10 + .09 - .15
 </code></pre>
 
-<pre><code>[1] 0.02
+<pre><code>[1] 0.04
 </code></pre>
 
 </div>
@@ -107,7 +107,7 @@ <h2>About these slides</h2>
 <ol>
 <li>1.00</li>
 <li>0.75</li>
-<li>0.50</li>
+<li><em>0.50</em></li>
 <li>0.25</li>
 </ol>
 

06_StatisticalInference/homework/hw1.md

@@ -25,27 +25,27 @@ Creating Data Products
 
 --- &radio
 
-Consider influenza epidemics for two parent heterosexual families. Suppose that the probability is 15% that at least one of the parents has contracted the disease. The probability that the father has contracted influenza is 6% while that the mother contracted the disease is 5%. What is the probability that both contracted influenza expressed as a whole number percentage?
+Consider influenza epidemics for two parent heterosexual families. Suppose that the probability is 15% that at least one of the parents has contracted the disease. The probability that the father has contracted influenza is 10% while that the mother contracted the disease is 9%. What is the probability that both contracted influenza expressed as a whole number percentage?
 
 1. 15%
-2. 6%
-3. 5%
-4. _2%_
+2. 10%
+3. 9%
+4. _4%_
 
 *** .hint
-$A = Father$, $P(A) = .06$, $B = Mother$, $P(B) = .05$ 
+$A = Father$, $P(A) = .10$, $B = Mother$, $P(B) = .09$ 
 $P(A\cup B) = .15$, 
 
 *** .explanation
-$P(A\cup B) = P(A) + P(B) - 2 P(AB)$ thus
-$$.15 = .06 + .05 - 2 P(AB)$$
+$P(A\cup B) = P(A) + P(B) - P(AB)$ thus
+$$.15 = .10 + .09 - P(AB)$$
 
 ```r
-(0.15 - .06 - .05) / 2
+.10 + .09 - .15
 ```
 
 ```
-[1] 0.02
+[1] 0.04
 ```
 
 
@@ -55,7 +55,7 @@ A random variable, $X$, is uniform, a box from $0$ to $1$ of height $1$. (So tha
 
 1. 1.00
 2. 0.75
-3. 0.50
+3. _0.50_
 4. 0.25
 
 *** .hint

06_StatisticalInference/homework/hw2.html

@@ -48,12 +48,11 @@ <h2>About these slides</h2>
   </hgroup>
   <article data-timings="">
     <ul>
-<li>These are some practice problems for Statistical Inference Quiz 1</li>
+<li>These are some practice problems for Statistical Inference Quiz 2</li>
 <li>They were created using slidify interactive which you will learn in 
 Creating Data Products</li>
 <li>Please help improve this with pull requests here
-(<a href="https://github.com/bcaffo/courses">https://github.com/bcaffo/courses</a>)
-runif(1)</li>
+(<a href="https://github.com/bcaffo/courses">https://github.com/bcaffo/courses</a>)</li>
 </ul>
 
   </article>
@@ -288,12 +287,12 @@ <h2>About these slides</h2>
 
 </div>
 <div class="quiz-explanation">
-  <p><span class="answer">89.1</span></p>
+  <p><span class="answer">10.9</span></p>
 
-<pre><code class="r">round(pbinom(4, prob = .5, size = 6, lower.tail = TRUE) * 100, 1)
+<pre><code class="r">round(pbinom(4, prob = .5, size = 6, lower.tail = FALSE) * 100, 1)
 </code></pre>
 
-<pre><code>[1] 89.1
+<pre><code>[1] 10.9
 </code></pre>
 
 </div>
@@ -388,9 +387,9 @@ <h2>About these slides</h2>
 
 </div>
 <div class="quiz-explanation">
-  <p>The answer will be <span class="answer">0</span> 
-since the variance of the sampling distribution of the mean is \(\sigma^2/12\)
-and the variance of a die roll is </p>
+  <p>The answer will be <span class="answer">0.292</span> 
+since the variance of the sampling distribution of the mean is \(\sigma^2/10\)
+where \(\sigma^2\) is the variance of a single die roll, which is </p>
 
 <pre><code class="r">mean((1 : 6 - 3.5)^2)
 </code></pre>

06_StatisticalInference/homework/hw2.md

@@ -16,12 +16,11 @@ mode        : selfcontained # {standalone, draft}
 
 
 ## About these slides
-- These are some practice problems for Statistical Inference Quiz 1
+- These are some practice problems for Statistical Inference Quiz 2
 - They were created using slidify interactive which you will learn in 
 Creating Data Products
 - Please help improve this with pull requests here
 (https://github.com/bcaffo/courses)
-runif(1)
 
 --- &radio
 The probability that a manuscript gets accepted to a journal is 12% (say). However,
@@ -182,15 +181,15 @@ Let $p=.5$ and $X$ be binomial
 
 *** .explanation
 
-<span class="answer">89.1</span>
+<span class="answer">10.9</span>
 
 
 ```r
-round(pbinom(4, prob = .5, size = 6, lower.tail = TRUE) * 100, 1)
+round(pbinom(4, prob = .5, size = 6, lower.tail = FALSE) * 100, 1)
 ```
 
 ```
-[1] 89.1
+[1] 10.9
 ```
 
 
@@ -247,9 +246,9 @@ If you roll ten standard dice, take their average, then repeat this process over
 $$Var(\bar X) = \sigma^2 /n$$
 
 *** .explanation
-The answer will be <span class="answer">0</span> 
-since the variance of the sampling distribution of the mean is $\sigma^2/12$
-and the variance of a die roll is 
+The answer will be <span class="answer">0.292</span> 
+since the variance of the sampling distribution of the mean is $\sigma^2/10$
+where $\sigma^2$ is the variance of a single die roll, which is 
 
 
 ```r

06_StatisticalInference/homework/hw3.Rmd

@@ -70,11 +70,11 @@ students t confidence interval touch zero?
 The t interval is $\bar x t_{.95, 8}\pm s /sqrt{n}$
 
 *** .explanation
-<span class="answer">`r round(qt(.95, df = 3) * 1 / 3, 2)`</span>
+<span class="answer">`r round(qt(.95, df = 8) * 1 / 3, 2)`</span>
 
 We want $\bar x = t_{.95} s / sqrt{n}$
 ```{r}
-round(qt(.95, df = 3) * 1 / 3, 2)
+round(qt(.95, df = 8) * 1 / 3, 2)
 ```
 
 
@@ -83,15 +83,15 @@ An independent group Student's T interval is used over
 a paired T interval when:
 
 1. The observations are paired between the groups.
-2. _The observations within the groups are natually assumed to be statistically independent_
+2. _The observations between the groups are natually assumed to be statistically independent_
 3. As long as you do it correctly, either is fine.
 4. More details are needed to answer this question
 
 *** .hint
 A paired interval is for paired observations.
 
 *** .explanation
-If the groups are independent is the correct interval.
+We can't pair them if the groups are independent of each other as well as independent within themselves.
 
 
 --- &multitext
@@ -132,7 +132,7 @@ C'mon. You don't need a hint
 
 *** .explanation
 This is just an example of what happens to confidence intervals as you
-increas the confidence level. You want to be quite sure in your interval (i.e.
+increase the confidence level. You want to be quite sure in your interval (i.e.
 have a large confidence level) and so you would increase the interval's width
 
 --- &radio
@@ -153,9 +153,9 @@ make sure the results make sense in the context of the problem.
 The interval was conducted subtracting 4 - 6 and was entirely above zero.
 
 --- &multitext
-Suppose that 18 obese subjects were randomized, 9 each, to a new diet pill and a placebo. Subjects' body mass indices (BMIs) were measured at a baseline and again after having received the treatment or placebo for four weeks. The average difference from follow-up to the baseline (followup - baseline) was ???3 kg/m2 for the treated group and 1 kg/m2 for the placebo group. The corresponding standard deviations of the differences was 1.5 kg/m2 for the treatment group and 1.8 kg/m2 for the placebo group. Does the change in BMI over the four week period appear to differ between the treated and placebo groups?  
+Suppose that 18 obese subjects were randomized, 9 each, to a new diet pill and a placebo. Subjects' body mass indices (BMIs) were measured at a baseline and again after having received the treatment or placebo for four weeks. The average difference from follow-up to the baseline (followup - baseline) was 3 kg/m2 for the treated group and 1 kg/m2 for the placebo group. The corresponding standard deviations of the differences was 1.5 kg/m2 for the treatment group and 1.8 kg/m2 for the placebo group. The study aims to answer whether the change in BMI over the four week period appear to differ between the treated and placebo groups. 
 
-1. Calculate the pooled variance estimate to 2 decimal places
+What is the pooled variance estimate? (to 2 decimal places)
 
 
 *** .hint
@@ -164,7 +164,6 @@ individual variances
 
 
 *** .explanation
-<span class="answer">`r round(min(confint), 1)`</span>
 ```{r}
 n1 <- n2 <- 9
 x1 <- -3  ##treated

06_StatisticalInference/homework/hw3.html

@@ -122,14 +122,14 @@ <h2>About these slides</h2>
 
 </div>
 <div class="quiz-explanation">
-  <p><span class="answer">0.78</span></p>
+  <p><span class="answer">0.62</span></p>
 
 <p>We want \(\bar x = t_{.95} s / sqrt{n}\)</p>
 
-<pre><code class="r">round(qt(.95, df = 3) * 1 / 3, 2)
+<pre><code class="r">round(qt(.95, df = 8) * 1 / 3, 2)
 </code></pre>
 
-<pre><code>[1] 0.78
+<pre><code>[1] 0.62
 </code></pre>
 
 </div>
@@ -147,7 +147,7 @@ <h2>About these slides</h2>
 
 <ol>
 <li>The observations are paired between the groups.</li>
-<li><em>The observations within the groups are natually assumed to be statistically independent</em></li>
+<li><em>The observations between the groups are natually assumed to be statistically independent</em></li>
 <li>As long as you do it correctly, either is fine.</li>
 <li>More details are needed to answer this question</li>
 </ol>
@@ -162,7 +162,7 @@ <h2>About these slides</h2>
 
 </div>
 <div class="quiz-explanation">
-  <p>If the groups are independent is the correct interval.</p>
+  <p>We can&#39;t pair them if the groups are independent of each other as well as independent within themselves.</p>
 
 </div>
 </div>
@@ -233,7 +233,7 @@ <h2>About these slides</h2>
 </div>
 <div class="quiz-explanation">
   <p>This is just an example of what happens to confidence intervals as you
-increas the confidence level. You want to be quite sure in your interval (i.e.
+increase the confidence level. You want to be quite sure in your interval (i.e.
 have a large confidence level) and so you would increase the interval&#39;s width</p>
 
 </div>
@@ -279,11 +279,9 @@ <h2>About these slides</h2>
   <article data-timings="">
 
 <div class="quiz-text quiz-multitext well">
-  <p>Suppose that 18 obese subjects were randomized, 9 each, to a new diet pill and a placebo. Subjects&#39; body mass indices (BMIs) were measured at a baseline and again after having received the treatment or placebo for four weeks. The average difference from follow-up to the baseline (followup - baseline) was ???3 kg/m2 for the treated group and 1 kg/m2 for the placebo group. The corresponding standard deviations of the differences was 1.5 kg/m2 for the treatment group and 1.8 kg/m2 for the placebo group. Does the change in BMI over the four week period appear to differ between the treated and placebo groups?  </p>
+  <p>Suppose that 18 obese subjects were randomized, 9 each, to a new diet pill and a placebo. Subjects&#39; body mass indices (BMIs) were measured at a baseline and again after having received the treatment or placebo for four weeks. The average difference from follow-up to the baseline (followup - baseline) was 3 kg/m2 for the treated group and 1 kg/m2 for the placebo group. The corresponding standard deviations of the differences was 1.5 kg/m2 for the treatment group and 1.8 kg/m2 for the placebo group. The study aims to answer whether the change in BMI over the four week period appear to differ between the treated and placebo groups. </p>
 
-<ol>
-<li>Calculate the pooled variance estimate to 2 decimal places</li>
-</ol>
+<p>What is the pooled variance estimate? (to 2 decimal places)</p>
 
   <button class="quiz-submit btn btn-primary">Submit</button>
   <button class="quiz-toggle-hint btn btn-info">Show Hint</button>
@@ -296,9 +294,7 @@ <h2>About these slides</h2>
 
 </div>
 <div class="quiz-explanation">
-  <p><span class="answer">3.2</span></p>
-
-<pre><code class="r">n1 &lt;- n2 &lt;- 9
+  <pre><code class="r">n1 &lt;- n2 &lt;- 9
 x1 &lt;- -3  ##treated
 x2 &lt;- 1  ##placebo
 s1 &lt;- 1.5  ##treated

06_StatisticalInference/homework/hw3.md

@@ -64,16 +64,16 @@ students t confidence interval touch zero?
 The t interval is $\bar x t_{.95, 8}\pm s /sqrt{n}$
 
 *** .explanation
-<span class="answer">0.78</span>
+<span class="answer">0.62</span>
 
 We want $\bar x = t_{.95} s / sqrt{n}$
 
 ```r
-round(qt(.95, df = 3) * 1 / 3, 2)
+round(qt(.95, df = 8) * 1 / 3, 2)
 ```
 
 ```
-[1] 0.78
+[1] 0.62
 ```
 
 
@@ -83,15 +83,15 @@ An independent group Student's T interval is used over
 a paired T interval when:
 
 1. The observations are paired between the groups.
-2. _The observations within the groups are natually assumed to be statistically independent_
+2. _The observations between the groups are natually assumed to be statistically independent_
 3. As long as you do it correctly, either is fine.
 4. More details are needed to answer this question
 
 *** .hint
 A paired interval is for paired observations.
 
 *** .explanation
-If the groups are independent is the correct interval.
+We can't pair them if the groups are independent of each other as well as independent within themselves.
 
 
 --- &multitext
@@ -134,7 +134,7 @@ C'mon. You don't need a hint
 
 *** .explanation
 This is just an example of what happens to confidence intervals as you
-increas the confidence level. You want to be quite sure in your interval (i.e.
+increase the confidence level. You want to be quite sure in your interval (i.e.
 have a large confidence level) and so you would increase the interval's width
 
 --- &radio
@@ -155,9 +155,9 @@ make sure the results make sense in the context of the problem.
 The interval was conducted subtracting 4 - 6 and was entirely above zero.
 
 --- &multitext
-Suppose that 18 obese subjects were randomized, 9 each, to a new diet pill and a placebo. Subjects' body mass indices (BMIs) were measured at a baseline and again after having received the treatment or placebo for four weeks. The average difference from follow-up to the baseline (followup - baseline) was ???3 kg/m2 for the treated group and 1 kg/m2 for the placebo group. The corresponding standard deviations of the differences was 1.5 kg/m2 for the treatment group and 1.8 kg/m2 for the placebo group. Does the change in BMI over the four week period appear to differ between the treated and placebo groups?  
+Suppose that 18 obese subjects were randomized, 9 each, to a new diet pill and a placebo. Subjects' body mass indices (BMIs) were measured at a baseline and again after having received the treatment or placebo for four weeks. The average difference from follow-up to the baseline (followup - baseline) was 3 kg/m2 for the treated group and 1 kg/m2 for the placebo group. The corresponding standard deviations of the differences was 1.5 kg/m2 for the treatment group and 1.8 kg/m2 for the placebo group. The study aims to answer whether the change in BMI over the four week period appear to differ between the treated and placebo groups. 
 
-1. Calculate the pooled variance estimate to 2 decimal places
+What is the pooled variance estimate? (to 2 decimal places)
 
 
 *** .hint
@@ -166,7 +166,6 @@ individual variances
 
 
 *** .explanation
-<span class="answer">3.2</span>
 
 ```r
 n1 <- n2 <- 9