Sampling Distribution of a Sample Mean: Learn It 1

  • Create a sampling distribution given [latex]\mu[/latex] and [latex]n[/latex].
  • Know and check the conditions of the Central Limit Theorem.
  • Use the normal approximation to compute probabilities involving sample means when appropriate.

We begin this module with a discussion of the sampling distribution of sample means. This will help us understand how sample means vary when we select random samples from a population with a known mean. Previously, we encountered similar ideas in order to understand the distribution of sample proportions.

A sampling distribution is the probability distribution of a sample statistic, such as a sample mean or sample proportion, as it varies from sample to sample.

Average Rental Prices

Airbnb is a website that connects people who are renting out rooms or homes with people looking for accommodations. The price depends on many factors, such as location, the booking window, prices, the popularity of a listing, the number of positive reviews, and more. What can we learn about different hosts and areas? What can we learn from predictions? Which hosts are the busiest and why? Is there any noticeable difference in traffic among different areas, and what could be the reason for it?[1]

A woman with luggage looking at the New York skyline.

Let’s explore the prices of Airbnb listings under $500 per night in New York City in 2019 and examine the behavior of sample mean prices for random samples of listings.[2]

So, what can we learn from the prices of Airbnb listings under $500 per night in New York City in 2019? What inferences can we conclude based on pricing variability? Can we utilize New York City’s data and compare the average prices with other cities?

  1. https://www.kaggle.com/datasets/dgomonov/new-york-city-airbnb-open-data ↵
  2. https://www.kaggle.com/datasets/dgomonov/new-york-city-airbnb-open-data ↵