This code challenge is designed to test your understanding of the Phase 2 material. It covers:
- Normal Distribution
- Statistical Tests
- Bayesian Statistics
- Linear Regression
Read the instructions carefully. You will be asked both to write code and to answer short answer questions.
We have provided some code tests for you to run to check that your work meets the item specifications. Passing these tests does not necessarily mean that you have gotten the item correct - there are additional hidden tests. However, if any of the tests do not pass, this tells you that your code is incorrect and needs changes to meet the specification. To determine what the issue is, read the comments in the code test cells, the error message you receive, and the item instructions.
For the short answer questions...
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Use your own words. It is OK to refer to outside resources when crafting your response, but do not copy text from another source.
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Communicate clearly. We are not grading your writing skills, but you can only receive full credit if your teacher is able to fully understand your response.
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Be concise. You should be able to answer most short answer questions in a sentence or two. Writing unnecessarily long answers increases the risk of you being unclear or saying something incorrect.
# Run this cell without changes to import the necessary libraries
import itertools
import numpy as np
import pandas as pd
from numbers import Number
from scipy import stats
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
import pickleIn this part, you will analyze check totals at a TexMex restaurant. We know that the population distribution of check totals for the TexMex restaurant is normally distributed with a mean of \$20 and a standard deviation of \$3.
Starter Code
z_score_26 =
# your code here
raise NotImplementedError# This test confirms that you have created a numeric variable named z_score_26
assert isinstance(z_score_26, Number)1.2) Create a numeric variable p_under_26 containing the approximate proportion of all checks that are less than \$26.
Hint: Use the answer from the previous question along with the empirical rule, a Python function, or this z-table.
Starter Code
p_under_26 =
# your code here
raise NotImplementedError# This test confirms that you have created a numeric variable named p_under_26
assert isinstance(p_under_26, Number)
# These tests confirm that p_under_26 is a value between 0 and 1
assert p_under_26 >= 0
assert p_under_26 <= 11.3) Create numeric variables conf_low and conf_high containing the lower and upper bounds (respectively) of a 95% confidence interval for the mean of one waiter's check amounts using the information below.
One week, a waiter gets 100 checks with a mean of \$19 and a standard deviation of \$3.
Starter Code
n = 100
mean = 19
std = 3
conf_low =
conf_high =
# your code here
raise NotImplementedError# These tests confirm that you have created numeric variables named conf_low and conf_high
assert isinstance(conf_low, Number)
assert isinstance(conf_high, Number)
# This test confirms that conf_low is below conf_high
assert conf_low < conf_high
# These statements print your answers for reference to help answer the next question
print('The lower bound of the 95% confidence interval is {}'.format(conf_low))
print('The upper bound of the 95% confidence interval is {}'.format(conf_high))YOUR ANSWER HERE
The TexMex restaurant recently introduced queso to its menu.
We have a random sample containing 2000 check totals, all from different customers: 1000 check totals for orders without queso ("no queso") and 1000 check totals for orders with queso ("queso").
In the cell below, we load the sample data for you into the arrays no_queso and queso for the "no queso" and "queso" order check totals, respectively.
# Run this cell without changes
# Load the sample data
no_queso = pickle.load(open('./no_queso.pkl', 'rb'))
queso = pickle.load(open('./queso.pkl', 'rb'))2.1) Short Answer: State null and alternative hypotheses to use for testing whether customers who order queso spend different amounts of money from customers who do not order queso.
YOUR ANSWER HERE
Your answer should be specific to this context, not a general statement of what Type I error is.
YOUR ANSWER HERE
2.3) Create a numeric variable p_value containing the p-value associated with a statistical test of your hypotheses.
You must identify and implement the correct statistical test for this scenario. You can assume the two samples have equal variances.
Hint: Use scipy.stats to calculate the answer - it has already been imported as stats. Relevant documentation can be found here.
Starter Code
p_value =
# your code here
raise NotImplementedError# These tests confirm that you have created a numeric variable named p_value
assert isinstance(p_value, Number)2.4) Short Answer: Can you reject the null hypothesis using a significance level of $\alpha$ = 0.05? Explain why or why not.
YOUR ANSWER HERE
A medical test is designed to diagnose a certain disease. The test has a false positive rate of 10%, meaning that 10% of people without the disease will get a positive test result. The test has a false negative rate of 2%, meaning that 2% of people with the disease will get a negative result. Only 1% of the population has this disease.
3.1) Create a numeric variable p_pos_test containing the probability of a person receiving a positive test result.
Assume that the person being tested is randomly selected from the broader population.
Starter Code
false_pos_rate = 0.1
false_neg_rate = 0.02
population_rate = 0.01
p_pos_test =
# your code here
raise NotImplementedError# This test confirms that you have created a numeric variable named p_pos_test
assert isinstance(p_pos_test, Number)
# These tests confirm that p_pos_test is a value between 0 and 1
assert p_pos_test >= 0
assert p_pos_test <= 13.2) Create a numeric variable p_pos_pos containing the probability of a person actually having the disease if they receive a positive test result.
Assume that the person being tested is randomly selected from the broader population.
Hint: Use your answer to the previous question to help answer this one.
Starter Code
false_pos_rate = 0.1
false_neg_rate = 0.02
population_rate = 0.01
p_pos_pos =
# your code here
raise NotImplementedError# This test confirms that you have created a numeric variable named p_pos_pos
assert isinstance(p_pos_pos, Number)
# These tests confirm that p_pos_pos is a value between 0 and 1
assert p_pos_pos >= 0
assert p_pos_pos <= 1In this section, you'll run regression models with advertising data. The dataset includes the advertising spending and sales for 200 products. These products are a random sample of 200 products from a larger population of products.
The dataset has three features - TV, radio, and newspaper - that describe how many thousands of advertising dollars were spent promoting the product. The target, sales, describes how many millions of dollars in sales the product had.
# Run this cell without changes
import statsmodels
from statsmodels.formula.api import ols
data = pd.read_csv('./advertising.csv').drop('Unnamed: 0', axis=1)
X = data.drop('sales', axis=1)
y = data['sales']4.1) Create a variable tv_mod_summ containing the summary of a fit StatsModels ols model for a linear regression using TV to predict sales.
Starter Code
tv_mod = ols(
tv_mod_summ = tv_mod.summary()
# your code here
raise NotImplementedError# This test confirms that you have created a variable named tv_mod_summ containing a StatsModels Summary
assert type(tv_mod_summ) == statsmodels.iolib.summary.Summary
# This statement prints your answer for reference to help answer the next question
print(tv_mod_summ)4.2) Short Answer: Is there a statistically significant relationship between TV advertising spend and sales in this model? How did you determine this from the model output?
This question is asking you to use your findings from the sample in your dataset to make an inference about the relationship between TV advertising spend and sales in the broader population.
YOUR ANSWER HERE
4.3) Short Answer: Run the cell below to produce a correlation matrix. Given the output, would you expect any collinearity issues if you included all of these features in one regression model?
# Run this cell
X.corr()YOUR ANSWER HERE
4.4) Create a variable all_mod_summ containing the summary of a fit StatsModels ols model for a multiple regression using TV, radio, and newspaper to predict sales.
Starter Code
all_mod = ols(
all_mod_summ = all_mod.summary()
# your code here
raise NotImplementedError# This test confirms that you have created a variable named all_mod_summ containing a StatsModels Summary
assert type(all_mod_summ) == statsmodels.iolib.summary.Summary
# This statement prints your answer for reference to help answer the next question
print(all_mod_summ)4.5) Short Answer: Does this model do a better job of explaining sales than the previous model using only the TV feature? Explain how you determined this based on the model output.
YOUR ANSWER HERE