What makes a good wine?

The goal of this homework is to continue practicing two-sample statistical inference using both simulation-based approaches. Use the lecture notes, readings, and application exercises to help you complete homework.

The Data

Today’s dataset has been adapted from a large data set of wine reviews from Kaggle. Reviews were scraped from WineEnthusiast, which contain information about both the wine itself as well as the reviewer’s description of that wine. Here, I provide a subset of the data. You may consider each of these observations to be an independent, representative sample of all wines.

The variables are as follows

country: the country that the wine is from (France, Italy, US)
points: the number of points WineEnthusiast rated the wine on a scale of 1-100.
price: cost for a bottle (USD)
variety: type of grapes used to make the wine
type: red or white wine
title: title of the wine review
description: reviewer’s description of the wine

Write all R code according to the style guidelines discussed in class.

To following resource provides code needed to make useful symbols. You may use the code to typeset the characters of interest in the narrative of your document:

$\mu$: $\mu$
$\alpha$: $\alpha$
$>$: $>$
$<$: $<$
$\neq$: $\neq$
$H_0$: $H_{0}$
$H_a$: $H_{a}$
$p_{group}$: $p_{group}$

Exercises

Overall hint: When performing a hypothesis test, you must provide the significance level of your test, the null and alternative hypotheses, the p-value, your decision, and an interpretation of the p-value in context of the original research question.

At the start of each exercise that requires simulation, set a random seed equal to the exercise number in the R chunk.

Make sure that your code is reproducible.

Part 0

The data are not pre-provided for you this week! Instead, you will add it to your GitHub hw-07-wine project yourself!

Go to Canvas $\Rightarrow$ Files and download the file called wines.csv. Locate this file on your local computer, usually found in your Downloads folder.

From your Math 118 folder you created for this course, find the hw-07-wine project folder corresponding to this homework. Now create a new data/ folder within this folder.
Within your new data/ folder, upload the wines.csv file.

You may now load in the data with the following code as per usual, where ____ should be replaced by a meaningful name of your choosing. Then remove eval = FALSE before you knit!

library(tidyverse)
library(infer)
____ <- read.csv("data/wines.csv")

Part 1

For this exercise alone, consider wines from the US and Italy only. Evaluate the hypothesis that the country where the wine is produced is independent of its type (red or white). Use a significance level of $\alpha = 0.05$. Visualize your null distribution.

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Part 2

Let’s say I’m doing to a nice dinner party, and I’m told to bring a bottle of wine. I want to bring an acceptable bottle, but I don’t like these friends enough to spend more than $20 on a bottle of wine. So I have to be strategic. I’ve been told that a cheap white is usually better than a cheap red, but that an expensive red is always better than an expensive white. Maybe I should buy a wine based on its points-to-price ratio.

Wrangle your data frame to create a new variable ratio, calculated as a wine’s points divided by its price.

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Wines with higher values for this ratio might indicate that the wine is a good deal. Comprehensively evaluate the hypothesis at the $\alpha = 0.05$ level that among wines that are at most $20 per bottle, white wines have a higher average point-to-price ratio compared to red wines. You do not need to visualize the null distribution.

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How would your decision and conclusion change if we used $\alpha = 0.10$ instead?

⊕Hint: refer back to the lectures about probability and the definition of Type I error to answer this question!

Suppose you perform 10 independent hypothesis tests at the $\alpha = 0.05$ level, and further suppose that in reality, the null hypothesis is TRUE for all 10 tests. What is the probability that you make at least one Type I error?

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Let’s say you just really hate white wine and are trying to demonstrate to others that it’s associated with lower ratings in terms of points. Describe the potential ethical ramifications of performing all of these tests and reporting only the significant results from the tests that support your narrative. Consider your answer from Exercise 5 in crafting this narrative.

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Submission

Knit to PDF to create a PDF document. Knit and commit all remaining changes, and push your work to GitHub. Make sure all files are updated on your GitHub repo.

Please upload your PDF document to Canvas.

HW 07: Wine