Quantifying uncertainty

An article in the The Asheville Citizen-Times published in the summer of 2020 claims that the average price per guest (ppg) for properties in Asheville is $60 on Airbnb. To evaluate their claim we will use a dataset on 50 randomly selected Asheville Airbnb listings in June 2020. These data can be found in data/asheville.csv.

Let’s load the packages we’ll use first.

library(tidyverse)
library(tidymodels)

And then the data.

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Hypotheses

• Your turn: Write out the correct null and alternative hypothesis. Do this in both words and in proper notation.

Add response here.

Observed data

Our goal is to use calculate the probability of a sample statistic at least as extreme as the one observed in our data if in fact the null hypothesis is true.

• Demo: Calculate and report the sample statistic below using proper notation.

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\[\bar{x} = 76.6\]

The null distribution

Let’s use simulation-based methods to conduct the hypothesis test specified above.

Generate

We’ll start by generating the null distribution.

• Demo: Generate the null distribution?

set.seed(4321)

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• Your turn: Take a look at null_dist. What does each element in this distribution represent?

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Visualize

• Question: Before you visualize the distribution of null_dist – at what value would you expect this distribution to be centered? Why?

Add response here.

• Demo: Create an appropriate visualization for your null distribution. Does the center of the distribution match what you guessed in the previous question?

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• Demo: Now, add a vertical red line on your null distribution that represents your sample statistic.

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• Question: Based on the position of this line, does your observed sample mean appear to be an unusual observation under the assumption of the null hypothesis?

Add response here.

p-value

Above, we eyeballed how likely/unlikely our observed mean is. Now, let’s actually quantify it using a p-value.

• Question: What is a p-value?

Add response here.

• Demo: Visualize the p-value.

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• Your turn: What is the p-value?

Add response here.

Conclusion

• Your turn: What is the conclusion of the hypothesis test based on the p-value you calculated? Make sure to frame it in context of the data and the research question. Use a significance level of 5% to make your conclusion.

Add response here.

• Demo: Interpret the p-value in context of the data and the research question.

Add response here.

Get real…

• Question: What we did above was a “toy example” to illustrate hypothesis test. What would you change to make this a real, more robust analysis?

Add response here.

• Demo: Work through the analysis again with these changes.

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