RPubs link information

https://rpubs.com/littlebravesri/s3774307

Introduction

• Airbnb is an online marketplace for renting accomodations.
• Available in 191 countries with various porperty and room types.
• Prices of accomodations are per night per person.
• According to Quartz, a business news organization, the average Airbnb rental rate in New York is said to be $160.47.
• Is this information accurate?

Problem Statement

• According to an article by the Inside Airbnb, there are 48,864 listings of rentals in the New York.
• With such information collected from different sources, an investigation can be performed to study if the given information is accurate or not.
• Out of the total population of Airbnbs available in New York, a sample can be collected to examine if enough statistical evidence is obtainable in order to conclude inferences about the population.
• Hypothesis Testing will be carried out to inspect if the average rental of New York Aribnb is exactly $160.47 or not.

Data

• The data collected for this investigation was retrieved from Tableau Public, an analytics company.
• There are 30478 listings in the data set with 13 information attributes about each listing.
• Since the aim of the analysis involves only the price, the other attributes are not considered for the Hypothesis Testing.
• The factors were converted from characters as preprocessing.

Data Cont.

• The variables and the final preprocessed types are as follows:
  • Host Id
  • Host Since (Date)
  • Name of the rental
  • Neighbourhood (Factors with 5 levels such as Bronx, Brooklyn, Manhattan, Queens, Staten Island)
  • Property Type (Factors with 19 levels such as Apartment, Villa, Townhouse, House, Dorm, etc.)
  • Room Type (Factors with 3 levels such as Entire home/apt, Private room, Shared room" )
  • Zipcode
    
  • Number of Beds in the rental
  • Number of Records
  • Number Of Reviews
  • Price
  • Review Scores Rating

Descriptive Statistics

• The variable of interest chosen for this invesitigation is Price.
• The remaining variables are not necesary for this analysis and hence are not considered.
• The summary statistics of Price is given below.
• It does not have any missing values and possible outliers and hence no action was taken.

airbnb %>% summarise(Min = min(Price, na.rm = TRUE),
                     Q1 = quantile(Price, probs = .25, na.rm = TRUE),
                     Median = median(Price, na.rm = TRUE), 
                     Q3 = quantile(Price, probs = .75, na.rm = TRUE),
                     Max = max(Price, na.rm = TRUE),
                     Mean = mean(Price, na.rm = TRUE),
                     SD = sd(Price, na.rm = TRUE),
                     n = n(),
                     Missing = sum(is.na(Price))) -> summary_table
knitr::kable(summary_table)

Visualisation

• From visualising the Price variable, it can be observed that it is right skewed.
• Most price range fall within $500 and $1000.

hist(airbnb$Price, breaks = 100)

Hypothesis Testing

The Null Hypothesis for this case would be that the average New York Airbnb rental price is equal to $160.47

\[H_0: \mu = 160.47 \] The Alternate Hypothesis would be that the average New York Airbnb rental price is not equal to $160.47

\[H_A: \mu \ne 160.47\]

Hypthesis Testing Cont.

• Regardless of having a right skewed distribution, on having a sample size (30478) greater than 30, by Central Limit Theorem, it can be considered/assumed that the price variable has a normal distribution.
• The entire data set can be considered as a single sample where a single variable is being focused on.
• Hence one sample t-test is used for testing the hypothesis.
• The mean price can be greater than or less than the hypothesised mean, therfore two tailed one sample t-test is the chosen Hypothesis Testing method.

Hypthesis Testing Cont.

# One sample t-test
t.test(airbnb$Price, mu = 160.47, conf.level = .95, alternative="two.sided")

## 
##  One Sample t-test
## 
## data:  airbnb$Price
## t = 2.7537, df = 30477, p-value = 0.005896
## alternative hypothesis: true mean is not equal to 160.47
## 95 percent confidence interval:
##  161.3692 165.8103
## sample estimates:
## mean of x 
##  163.5897

Hypthesis Testing Cont.

• The test statistics is 2.7537
• Significance level used is 0.05
• p-value of the result is 0.005896
• 95% confidence interval is between 161.3692 and 165.8103
• Sample mean price is 163.5897

Discussion

• The main aim of the investigation is the find if the mean price of New York Airbnb is $160.47 or not.
• A two-tailed, one-sample t-test was used to determine if the mean price was significantly different from the average price stated in the internet.
• The results of the t-test describes the p-value to be less than the significance level and the confidence interval does not capture the assumed value.
• The mean price is statistically significantly greater than the assumed population mean price.
• Hence, it can be concluded that the average price of New York Airbnb is not $160.47 in fact it is greater.

References

• Data source
  • https://public.tableau.com/en-us/s/resources
• Information on New York Airbnb
  • https://qz.com/779121/airbnb-vs-hotel-cost-comparison-you-can-rent-an-entire-home-on-airbnb-for-the-price-of-a-hotel-room/
  • https://muchneeded.com/airbnb-statistics/
  • http://insideairbnb.com/new-york-city/
  • https://www.quora.com/How-do-the-prices-on-Airbnb-work-Are-they-per-person-or-per-night
  • https://newonlinecourses.science.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing/examples