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You are given an array of numerical values, bootstrap samples, and size for a confidence interval.

Write a function that performs bootstrap sampling on the given array and calculates the confidence interval based on the given size.

Note: The function should return a tuple containing the minimum and maximum values of the confidence interval rounded to the tenths place.

Example

Input:

<pre tabindex="0" class="chroma"><code>values = [1, 2, 3, 4, 5]
</code></pre>

Output

<pre tabindex="0" class="chroma"><code>bootstrap_conf_interval(values, 1000, 0.95) -&gt; (1.2, 4.8)
</code></pre>

In this case, the function returns a tuple indicating that we are 95% confident that the population parameter lies between 1.2 and 4.8 based on our bootstrap samples.

Note: Results may vary due to the randomness of bootstrap sampling.

Write a function to bootstrap the confidence interface for a list of integers

Bootstrapping Confidence Intervals

Let’s say that there are six people trying to divide up into two equally separate teams. Because they want to pick random teams, on each round, each person shows their hand in either a face-up or face-down position. If there are three of each position, then they’ll split into teams. 

What’s the expected number of rounds that everyone will have to pick a hand side before they split into teams?

Estimated Rounds

Build a $k$ Nearest Neighbors classification model from scratch with the following conditions:

<ul>
<li>Use Euclidian distance (aka, the “2 norm”) as your closeness metric</li>
<li>Your function should be able to handle data frames of arbitrary many rows and columns</li>
<li>If there is a tie in the class of the $k$ nearest neighbors, rerun the search using $k-1$ neighbors instead</li>
<li>You may use <code>pandas</code> and <code>numpy</code> but NOT <code>scikit-learn</code></li>
</ul>

Example:

Input:

<pre><code class="language-python"><pre tabindex="0" class="chroma"><code>k = 5
new_point = [0.5,-2,8]
print(data)
...
 Var1 Var2 Var3 Target
0 -3.279536 3.362223 2.847892 2
1 -0.791565 1.742475 2.151587 2
2 -0.785992 -0.938681 -0.459770 0
3 -1.068190 1.461051 0.127130 3
4 -0.367568 -0.870240 -0.225734 0
.. ... ... ... ...
95 -1.327175 1.971085 -0.690689 2
96 -3.203714 1.847649 0.778901 2
97 -0.587640 0.647458 2.094385 2
98 0.363644 -0.509795 2.514191 1
99 -0.673498 2.955285 2.102122 4

[100 rows x 4 columns]
</code></pre></code></pre>

Output:

<pre><code class="language-python"><pre tabindex="0" class="chroma"><code>def kNN(k, new_point, data) -&gt; 2
</code></pre></code></pre>

Build a k Nearest Neighbors classification model from scratch.

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