Khan Academy AP Statistics
Paulo works at the United Nations. He researched what percent of the world's population lives on each continent. He surveys a sample of employees at the United Nations about their continent of origin to see if the distribution in the sample agrees with the percentages he researched.
A \chi^2χ 2 goodness of fit test
Ying's favorite candy is available with or without peanuts. He wonders if the color distribution is the same for both varieties, so he buys a large bag with peanuts and a large bag without peanuts and tallies the colors in each bag.
A \chi^2χ 2 test for homogeneity
A market researcher wondered if there was a relationship between a person's age and which media streaming service they preferred. The researcher obtained a random sample of people and categorized each of them as a teen or adult. They also categorized each person based on their preferred streaming service.
A \chi^2χ 2 test of independence
A test prep course takes a random sample of 505050 of its customers. Researchers score each customer on a diagnostic test before taking the course and again on a similar test after taking the course. They want to use these results to estimate the average difference between the before and after scores.
A paired ttt-interval for the mean difference
Apgar score is a number between 000 and 101010 that gives a measure of the physical condition of a newborn infant. Researchers collected the Apgar scores of 202020 sets of identical twins to test if the first-born twin's score was, on average, different than the second-born twin's score.
A paired ttt-test for the mean difference
The coach of a swimming team wonders if a new swim cap will make their team swim faster than their existing caps. The coach has each swimmer complete two laps—one with the new cap and one with their existing cap (in a random order). They want to test if, on average, the times are lower with the new caps.
A paired ttt-test for the mean difference
A website streams movies and television shows to millions of users. Employees know that the average time a user spends per session on their website is 222 hours. The website changed its design, and they wanted to know if the average session length was longer than 222 hours. They randomly sampled 100100100 users and recorded their session lengths
A t-test for mean
Felipe is curious if there is a relationship between a runner's age and their finishing time in a recent marathon. He takes a random sample of finishers and records the age (in years) and the finishing time (in minutes) for each of those sampled.
A ttt-test for slope
A food scientist wants to estimate the difference between the weights of eggs classified as jumbo and large. They plan on taking a sample of eggs of each type and comparing the average weight between the samples.
A two-sample ttt-interval for the difference of means
Raul lives in Richmond and his brother Alejandro lives in Aberdeen. They both complained about the high prices of avocados where they live, so they wondered if, on average, avocados were more expensive in one of their cities. Each of them took a random sample of shops in their city and got the price of avocado from each shop.
A two-sample ttt-test for the difference of means
Angelica surveyed 150150150 people in the 20\text{-}2920-2920, negative, 29 age group and 150150150 people in the 30\text{-}3930-3930, negative, 39 age group about whether or not they were vegetarian. She wants to estimate the difference between the percentage of people in each group who are vegetarian.
A two-sample zzz-interval for the difference of proportions
Julian wanted to know if he was better at bottle-flipping with his right hand or his left hand. He attempted 100100100 flips with each hand and counted how many successes he had with each hand.
A two-sample zzz-test for the difference of proportions
Data from a previous census says that 13\%13%13, percent of US citizens are foreign-born. A researcher wondered if that figure was still true, so they took a random sample of 100010001000 citizens. They observed 123123123 who were foreign-born and 877877877 who weren't.
a Z-test for proportion
Researchers were studying how playing a dancing video game impacts heart rate. They measured the heart rates (in beats per minute) of 151515 subjects before they danced a song and again after they finished dancing the song. They want to use these results to estimate the average difference between before and after heart rates.
a paired t interval for mean difference
A company makes a phone in 333 different colors. Tabitha wonders if an equal proportion of customers buy each color. She takes a random sample of 500500500 owners of this phone and records what color they have.
goodness of fit
Marta runs a website, and she knows that almost all visitors arrive to her site from a web search, from social media, or directly by entering the website's address. She made a change to the website, and she wonders if it impacted the ways people navigate to the site. She took a random sample of 500500500 visits before she made the change, and a separate random sample of 500500500 visits after she made the change.
homogeneity
Harisha is studying housing costs in his area. He wants to estimate how much monthly rent for an apartment tends to increase as the size of the apartment increases. He takes a random sample of apartments in his area and records the monthly cost of rent and the size (in square meters) of each apartment.
slope
A college professor wonders if there is a relationship between how long students spend on their midterm exam and their resulting score. The professor picks a random sample of students to observe and notes each of their times (in minutes) and their scores (from 000 to 100100100).
slope test
Kiera is researching the relationship between social media usage and sleep. She wants to estimate how much nightly sleep amounts increase or decrease as social media usage increases. She takes a random sample of people and asks each of them how many hours they slept last night and how many hours they used social media that day.
slope test
People applying for a driver's license In California usually need to take a multiple choice test as a part of the application process. An administrator of these tests wants to estimate the average number of questions that people get correct on the test. They take a random sample of scores from 100100100 testers.
t interval for a mean
Rex wants to estimate the average finishing time of the approximately 50{,}00050,00050, comma, 000 finishers at the New York City Marathon. He takes a random sample of finishers and records their times.
t interval for mean
A school counselor suspects that, on average, students at their school are sleeping less than 888 hours per night. They survey a random sample of students about how many hours they slept the previous night to see if their average sleep amount is significantly less than 888 hours.
t test for mean
Do people pick random numbers uniformly? Kiley asked 100100100 randomly selected people to pick a random whole number from 111 to 101010 and tallied how often each number was chosen.
x^2 goodness of fit
According to the distributor of a kind of trading card, 66\%66%66, percent of the cards are common, 25\%25%25, percent are uncommon, and 9\%9%9, percent are rare. Avery wondered if the rarity levels of the cards she and her friends owned followed this distribution, so she took a random sample of 500500500 cards and recorded their rarity levels.
x^2 goodness of fit test
The owners of a large shopping complex wondered if there was a relationship between how customers traveled to the complex and whether or not they made a purchase. They observed a random sample of 100100100 customers and categorized each of them based on transportation method and whether or not they made a purchase.
x^2 test of independence
Finn blogs about video games. In a particular game, a certain enemy occasionally drops a rare item when they are defeated. Finn wants to estimate the likelihood that this enemy drops the rare item, so he defeats the enemy 100010001000 times and tallies how many times the rare item is dropped.
z interval for proportion
Lylah created an app, and she recently updated the app. She randomly samples a group of users to estimate what percentage of all users are using the updated version.
z interval for proportion
A principal wondered if more than 50\%50%50, percent of students at their school bring a lunch from home rather than eating the lunch offered by the cafeteria. The principal observed 100100100 randomly selected students and noticed that 585858 brought their own lunch and 424242 ate the cafeteria lunch.
z test of proportion