diff --git a/docs/fa23-final/index.html b/docs/fa23-final/index.html
index a28a756..95398d5 100644
--- a/docs/fa23-final/index.html
+++ b/docs/fa23-final/index.html
@@ -275,7 +275,7 @@ <h3 id="problem-2.1">Problem 2.1</h3>
 given credit. Pick one of the two.</em></p>
 <p><strong>Simulation procedure</strong>:</p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> A. <code>np.random.choice([0, 1], bus.shape[0])</code></p></li>
+<li><p><input type="radio" disabled="" /> A. <code>np.random.choice([-1, 1], bus.shape[0])</code></p></li>
 <li><p><input type="radio" disabled="" /> B.
 <code>np.random.choice(bus['late'], bus.shape[0], replace = True)</code></p></li>
 <li><p><input type="radio" disabled="" /> C. Randomly permute the <code>'late'</code> column</p></li>
@@ -329,14 +329,14 @@ <h3 id="problem-2.2">Problem 2.2</h3>
 statistic were given credit. Pick one of the two.</em></p>
 <p><strong>Simulation procedure</strong>:</p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> A. <code>np.random.choice([0, 1], bus.shape[0])</code></p></li>
+<li><p><input type="radio" disabled="" /> A. <code>np.random.choice([-1, 1], bus.shape[0])</code></p></li>
 <li><p><input type="radio" disabled="" /> B.
 <code>np.random.choice(bus['late'], bus.shape[0], replace = True)</code></p></li>
 <li><p><input type="radio" disabled="" /> C. Randomly permute the <code>'late'</code> column</p></li>
 </ul>
 <p><strong>Test statistic</strong></p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> A. Number of values below <span class="math inline">1</span></p></li>
+<li><p><input type="radio" disabled="" /> A. Number of values below <span class="math inline">0</span></p></li>
 <li><p><input type="radio" disabled="" /> B. <code>np.mean</code></p></li>
 <li><p><input type="radio" disabled="" /> C. <code>np.std</code></p></li>
 <li><p><input type="radio" disabled="" /> D. TVD</p></li>
@@ -361,14 +361,14 @@ <h1 class="title"> </h1>
 population, which is just all buses. We then want to see if a sample is
 from that population, so we conduct a hypothesis test under the null.
 The null would be that buses are equally likely to be early or late, so
-we can simulate this by randomly generating <code>[0, 1]</code> for all
+we can simulate this by randomly generating <code>[-1, 1]</code> for all
 buses. This is what option A) does. <strong>Test statistic</strong>:
 Since we know the number of buses, we can use the number of values below
-<span class="math inline">1</span> to determine whether we have more
+<span class="math inline">0</span> to determine whether we have more
 early buses, more late buses, or the same amount. Similarly, the mean
-will give us a value between <span class="math inline">0</span> and
-<span class="math inline">1</span>, where <span class="math inline">0.5</span> means we have the equal early and late
-buses, while <span class="math inline">0</span> represents only early
+will give us a value between <span class="math inline">-1</span> and
+<span class="math inline">1</span>, where <span class="math inline">0</span> means we have the equal early and late
+buses, while <span class="math inline">-1</span> represents only early
 buses, and <span class="math inline">1</span> represents only late
 buses.</p>
 </div>
@@ -381,7 +381,7 @@ <h3 id="problem-2.3">Problem 2.3</h3>
 <code>'line'</code> column?</p>
 <p><strong>Simulation procedure</strong>:</p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> A. <code>np.random.choice([0, 1], bus.shape[0])</code></p></li>
+<li><p><input type="radio" disabled="" /> A. <code>np.random.choice([-1, 1], bus.shape[0])</code></p></li>
 <li><p><input type="radio" disabled="" /> B.
 <code>np.random.choice(bus['late'], bus.shape[0], replace = True)</code></p></li>
 <li><p><input type="radio" disabled="" /> C. Randomly permute the <code>'late'</code> column</p></li>
@@ -427,7 +427,7 @@ <h3 id="problem-2.4">Problem 2.4</h3>
 <code>'time'</code> column?</p>
 <p><strong>Simulation procedure</strong>:</p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> A. <code>np.random.choice([0, 1], bus.shape[0])</code></p></li>
+<li><p><input type="radio" disabled="" /> A. <code>np.random.choice([-1, 1], bus.shape[0])</code></p></li>
 <li><p><input type="radio" disabled="" /> B.
 <code>np.random.choice(bus['late'], bus.shape[0], replace = True)</code></p></li>
 <li><p><input type="radio" disabled="" /> C. Randomly permute the <code>'late'</code> column</p></li>
diff --git a/problems/fa23-final/fa23-final-q03.md b/problems/fa23-final/fa23-final-q03.md
index f36a81a..de6cda2 100644
--- a/problems/fa23-final/fa23-final-q03.md
+++ b/problems/fa23-final/fa23-final-q03.md
@@ -7,7 +7,7 @@ Are buses more likely to be late in the morning (before $12$pm) or the afternoon
 
 **Simulation procedure**:
 
-( ) A. `np.random.choice([0, 1], bus.shape[0])`
+( ) A. `np.random.choice([-1, 1], bus.shape[0])`
 ( ) B. `np.random.choice(bus['late'], bus.shape[0], replace = True)`
 ( ) C. Randomly permute the `'late'` column
 
@@ -33,13 +33,13 @@ Are buses equally likely to be early or late?
 
 **Simulation procedure**:
 
-( ) A. `np.random.choice([0, 1], bus.shape[0])`
+( ) A. `np.random.choice([-1, 1], bus.shape[0])`
 ( ) B. `np.random.choice(bus['late'], bus.shape[0], replace = True)`
 ( ) C. Randomly permute the `'late'` column
 
 **Test statistic**
 
-( ) A. Number of values below $1$
+( ) A. Number of values below $0$
 ( ) B. `np.mean`
 ( ) C. `np.std`
 ( ) D. TVD
@@ -48,9 +48,9 @@ Are buses equally likely to be early or late?
 **Answer**: Simulation procedure - A). Test statistic - A) or B).
 
 **Simulation procedure**:
-We now have only one population, which is just all buses. We then want to see if a sample is from that population, so we conduct a hypothesis test under the null. The null would be that buses are equally likely to be early or late, so we can simulate this by randomly generating `[0, 1]` for all buses. This is what option A) does. 
+We now have only one population, which is just all buses. We then want to see if a sample is from that population, so we conduct a hypothesis test under the null. The null would be that buses are equally likely to be early or late, so we can simulate this by randomly generating `[-1, 1]` for all buses. This is what option A) does. 
 **Test statistic**:
-Since we know the number of buses, we can use the number of values below $1$ to determine whether we have more early buses, more late buses, or the same amount. Similarly, the mean will give us a value between $0$ and $1$, where $0.5$ means we have the equal early and late buses, while $0$ represents only early buses, and $1$ represents only late buses.
+Since we know the number of buses, we can use the number of values below $0$ to determine whether we have more early buses, more late buses, or the same amount. Similarly, the mean will give us a value between $-1$ and $1$, where $0$ means we have the equal early and late buses, while $-1$ represents only early buses, and $1$ represents only late buses.
 # END SOLN
 # END SUBPROB
 
@@ -59,7 +59,7 @@ Is the `'late'` column MAR dependent on the `'line'` column?
 
 **Simulation procedure**:
 
-( ) A. `np.random.choice([0, 1], bus.shape[0])`
+( ) A. `np.random.choice([-1, 1], bus.shape[0])`
 ( ) B. `np.random.choice(bus['late'], bus.shape[0], replace = True)`
 ( ) C. Randomly permute the `'late'` column
 
@@ -84,7 +84,7 @@ Is the `'late'` column MAR dependent on the `'time'` column?
 
 **Simulation procedure**:
 
-( ) A. `np.random.choice([0, 1], bus.shape[0])`
+( ) A. `np.random.choice([-1, 1], bus.shape[0])`
 ( ) B. `np.random.choice(bus['late'], bus.shape[0], replace = True)`
 ( ) C. Randomly permute the `'late'` column