Ace the free response questions on your AP Statistics exam with practice FRQs graded by Kai. Choose your subject below.
Knowt can make mistakes. Consider checking important information.
The best way to get better at FRQs is practice. Browse through dozens of practice AP Statistics FRQs to get ready for the big day.
Advertisement Design Impact on Customer Recall
A marketing company wants to test whether two different advertisement designs lead to differences in
Analyzing Z-Scores and Normal Distribution
Assume that a particular set of data is normally distributed with a mean of 100 and a standard devia
Basketball Free Throw Percentage Confidence Interval
A basketball player takes 80 free throws and makes 60 of them. Answer the following parts:
BMI and Blood Pressure Regression Analysis
A study examines the relationship between body mass index ($$BMI$$) and systolic blood pressure for
Boxplot Construction from Exam Scores
Consider the following set of exam scores: $$\{15, 18, 22, 24, 24, 25, 27, 29, 30, 32, 35\}$$ Answ
Categorical Data Analysis: Survey on Preferred School Year Length
A survey of 2000 parents asked about their preference for the length of the school year. The respons
Cumulative Frequency Analysis of Age Distribution
A study compares the age distributions of two different years using cumulative frequency plots. In Y
Customer Service Call Duration
Customer service call durations are approximately normally distributed with a mean of $$8$$ minutes
Effects of Multiplicative Transformations on Test Scores
A data set representing test scores is given as follows: {45, 55, 67, 73, 82, 88, 90}. Answer the fo
Employee Salary Adjustments
A company has six employees with the following salaries (in dollars): $$\{3000, 7000, 15000, 22000,
Event Attendance by Invitation Type
An event organizer tracked attendance based on invitation type (Digital, Paper) and the outcome (Att
Home Run Distances in Ballparks
The following set of home run distances (in feet) to center field in 13 ballparks is given: {387, 40
Impact of an Outlier on Summary Statistics
Consider the data set: {22, 25, 27, 30, 32, 150}, where the value 150 is a potential outlier. Answer
Interquartile Range and Boxplot Construction
Given the dataset: {12, 15, 16, 18, 20, 22, 25, 27, 30, 35}, perform an analysis of its distribution
Investigative Analysis of Public Health Survey on COVID-19
A public health survey was conducted with 500 adults to assess COVID-19 vaccination status, experien
Machine Reliability Testing
A machine is tested repeatedly for failure. The probability that the machine fails on any given test
Marketing Campaign Reach by Region
A company tracked responses to a marketing campaign in two regions (Region 1 and Region 2) categoriz
NBA Team Wins: Distribution Assessment
The numbers of wins for NBA teams in two conferences are summarized using comparative data displays.
NBA Wins: Analyzing Back-to-Back Stem Plots
A back-to-back stem plot displays the number of wins for NBA teams from the Eastern and Western Conf
Product Return Rates Across Regions
A company tracks product returns across four regions (North, South, East, West) with outcomes 'Retur
Public Transportation Usage by Occupation
A survey of 240 workers recorded their public transportation usage (Regular, Occasional, Never) alon
Salary Analysis: Effect of Raises on Mean Salary
A company has six employees whose current salaries are $$3000$$, $$7000$$, $$15000$$, $$22000$$, $$2
Simulation of the Sampling Distribution of the Mean Number of AP Classes Taken
A study of 2200 high school seniors reports the number of AP classes taken as follows: 0 AP classes
Social Media Engagement Analysis
A social media post is viewed by 200 users, and each user independently has a 5% chance of liking th
Stemplot Construction: Analyzing a Data Set
A dataset of 11 numbers is provided as follows: {12, 15, 15, 17, 17, 18, 20, 22, 22, 23, 25}.
Temperature and Reaction Rate Regression
A chemical kinetics experiment measured the reaction rate (in mol/sec) at different temperatures (in
Treatment Outcomes in Hospital Study
A hospital conducted a study on two treatments (Treatment X and Treatment Y) to evaluate patient out
Unit Conversion Impact on Summary Statistics
A data set representing the lengths of objects is given in inches: {12, 24, 36, 48, 60}. Answer the
Advertising Campaign and Sales Analysis
A company tracked the number of social media impressions (in thousands, x) and corresponding product
Bootstrap Simulation for the Regression Intercept's Sampling Distribution
A data analyst uses the bootstrap method to approximate the sampling distribution of the regression
Calculation of Correlation and Linear Regression from Summary Statistics
A study examines the relationship between daily device usage (in hours, X) and a productivity score
Coffee Shop Drink Preference
A survey at a coffee shop collected responses from 120 customers regarding two categorical variables
Constructing a Contingency Table from Raw Data
A researcher surveying 100 individuals collected the following raw counts regarding gender (Male, Fe
Correlation and Coefficient of Determination in Exam Performance
A researcher studying exam performance collected data on the number of hours students studied (X) an
Customer Satisfaction Survey
A retail store surveyed customers regarding their visit frequency (Frequent vs. Infrequent) and over
Customer Service and Order Mode Inference
In a survey at a local restaurant, 70 customers ordered online and 30 ordered in-person. Among the o
Effect of Advertisement Frequency on Brand Recognition
A marketing study was conducted to analyze the relationship between the number of advertisements see
Effectiveness of a New Curriculum
A school district implemented a new curriculum in some of its schools and maintained the traditional
Environmental Study: Air Pollution vs. Respiratory Issues
A public health researcher collects data from 50 cities to examine the relationship between air poll
Environmental Study: Temperature and Ice Cream Sales
An environmental study tracked ice cream sales (in hundreds of dollars) and the daily high temperatu
Evaluating Housing Market Trends Through Transformation
A real estate analyst studies the relationship between house square footage (x) and sale price (y, i
Experience and Salary: Exploring a Nonlinear Relationship
An HR department collects data on the number of years of experience (x) and annual salary (in thousa
Fitness Program Enrollment
A local gym evaluated enrollment trends by comparing two program types (Yoga vs. CrossFit) and atten
Impact of Study Environment on Academic Achievement
A survey of 100 students collected data on their study environment (categorized as 'Quiet' or 'Noisy
Job Training and Post-Training Wages
A job training program collected data from 30 participants on the number of training hours (x) and p
Manufacturing Defects in Two Production Lines
A manufacturing company operates two production lines. A quality control inspection was performed on
Online Learning Preferences
A survey was conducted among 200 students to determine their preferences for online learning. Studen
Simulating the Sampling Distribution of the Sample Mean in Bivariate Data
A study collects data on the number of study hours (x) and exam scores (y) for 100 students. Researc
Simulation of Bivariate Data with Varying Leverage Effects on Regression Coefficients
A researcher simulates bivariate data to explore how the presence of high-leverage points affects th
Simulation of the Impact of Measurement Error on the Sampling Distribution of Pearson's r
A study measures the relationship between two variables, but with varying degrees of measurement err
Temperature and Ice Cream Sales
A study over 30 days recorded the average daily temperature (in °F) and corresponding ice cream sale
Analysis of Boxplots from an Experiment on Pulse Rates
Researchers conducted an experiment comparing the effects of three beverages (coffee, caffeinated co
Commute Time and Job Satisfaction
A consulting firm conducts a study to examine whether longer commute times (in minutes, x) are assoc
Comparing Treatment Efficacy in a Retrospective Study
A retrospective observational study was conducted to examine the efficacy of two treatments for a pa
Customer Feedback for a New Product
A technology company collected customer feedback regarding a new product via two purchasing channels
Data Collection in a Prospective Observational Study
A hospital conducts a prospective study to evaluate recovery times following a specific surgical pro
Designing a Prospective Study for a Drug Trial
A pharmaceutical company is testing a new drug for lowering blood pressure. The study will involve f
Diet, Weight Loss, and Regression Analysis
A nutritionist is studying the relationship between daily caloric intake (Calories) and observed wei
Evaluating Bias in a Sampling Process: Voluntary Survey
A city council conducts a voluntary online survey regarding community safety. Out of 150 responses,
Impact of a New Diet on Blood Pressure
A health clinic is investigating whether a new diet can reduce systolic blood pressure. Patients are
Impact of Advertising on Sales Revenue
A chain of retail stores seeks to understand the relationship between advertising expenditures (in $
Internet Usage and Education Level
A study analyzed internet usage frequency (Daily, Weekly, Rarely) among individuals with different e
Interpreting Observational Study Data on Exercise and Blood Pressure
A study tracks daily exercise minutes and resulting changes in blood pressure for 100 adults over a
Matched Pairs Design in Educational Research
A school district is evaluating two teaching methods by having the same students experience both met
Physical Activity and Cognitive Function in Older Adults
Researchers are investigating whether increased physical activity is associated with better cognitiv
Remote Learning Effectiveness
At a high school, the impact of transitioning to remote learning on student test scores is studied u
Replication in Experimental Designs: Water Purification Study
Researchers are testing various water purification techniques in an experimental study. Replication
Simulating Sampling Distributions for Quality Control in Manufacturing
A manufacturing company produces items that are expected to weigh $$500 \text{ g}$$ on average with
Systematic Sampling in a Traffic Accident Study
A city transportation department wants to assess the frequency of traffic accidents at intersections
Teaching Methods and Student Performance
A school wants to compare the effectiveness of two different teaching methods on student performance
Urban Green Spaces and Air Quality
An urban planning study is being conducted to determine whether proximity to green spaces is associa
Voting Preference Analysis
A political analyst collected data on voting preferences by age group. The table below shows the num
Carnival Game Payoff Transformation
In a carnival game, the payoffs are: $$2$$ dollars with probability $$0.5$$, $$5$$ dollars with prob
Casino Chips: Sum and Variance Calculation
At a casino, couples receive free chips by drawing a card from two bags. One bag (X) contains the va
City Traffic Speed Analysis
The city transportation department collected data on the speeds of vehicles on a major highway. A ra
Comparing Consumer Spending at Two Malls
Two shopping malls record the average spending per visitor. Mall A has a sample of 100 visitors with
Comparing Daily Step Counts: Traditional Pedometer vs Fitness Tracker
A study compared the daily step counts of two groups: one group used a traditional pedometer (n = 50
Comparing Manufacturing Processes for Defect Reduction
An industrial engineer is comparing two manufacturing processes to determine which one produces fewe
Defect Rate Comparison between Two Factories
A manufacturing company is studying defect rates in two of its factories. Factory 1 produced 1000 it
Drug Effectiveness Study
Researchers conducted a clinical trial comparing a new drug to a placebo. The recovery outcomes are
Effects of Outliers on Sampling Distributions
A simulation study involves drawing samples from a dataset that contains outliers. For each sample,
Employee Training and Department Performance
A company recorded the outcomes of a recent employee training program across three departments. The
Exam Score Cumulative Distribution
The following table displays the distribution of scores on an exam from 200 students:
First Honest Encounter: Geometric Distribution
In ancient Greece, suppose only 12% of men are honest. Let \(X\) represent the trial on which the fi
Hospital ER Wait Times
A hospital is interested in assessing the average wait time in its emergency room. In a random sampl
Impact of Study Habits on Test Scores
A teacher wants to examine if spending an extra 30 minutes reviewing material after class influences
Investigative Study on Public Health Intervention
A local government is assessing the effectiveness of a new public health campaign aimed at reducing
Raffle Ticket Payouts in a Fundraiser
A charity raffle sells 500 tickets at $2 each. There is one main prize of $800 and two smaller prize
Rare Defects and Poisson Approximation
A factory produces electronic components with a defect rate of 0.002. In a shipment of 2000 units, l
Retail Customer Purchases: Random Variable Analysis
A survey at a retail store reveals that the number of items purchased per visit follows this distrib
Sampling Distribution of the Sample Mean from a Normal Population
A simulation experiment draws repeated random samples from a normally distributed population with $$
Social Media Usage Patterns by Age Group
A study surveyed 300 social media users to determine their preferred platform. The respondents were
Student Study Hours and Exam Performance Regression Analysis
A researcher examines the relationship between the number of hours a student studies (x) and their e
Student Testing Strategy and Scores Analysis
A standardized literacy test consists of 100 multiple-choice questions. When uncertain, test takers
Suit Name Letter Count
A card is drawn from a standard 52-card deck. Let the random variable $$X$$ be the number of letters
Survey Response Binomial Analysis
In a survey of $$50$$ respondents, each respondent has a $$0.65$$ probability of giving a positive r
The Impact of Sample Size on Outcome Predictability
A game organizer is designing a carnival game that involves tossing a fair coin. A player wins if th
Voter Turnout in Two Cities
A researcher collected data on the number of people who voted in two cities during an election. In C
Bacterial Count in Water Samples
A water quality test measures the concentration of bacteria (in CFU per 100 ml) in a river. The popu
Biased Estimator in Quality Control
A manufacturer uses an estimator to measure the maximum strength of a new material. A simulation of
Caffeine Content Analysis in Energy Drink Boxes
An energy drink contains caffeine distributed with a mean of 200 mg and a standard deviation of 10 m
Central Limit Theorem in Action: Distribution of Household Incomes
In a large metropolitan area, household incomes are highly skewed. A research team takes repeated ra
Central Limit Theorem in Customer Service Times
In a call center, individual call durations are skewed with an average of $$\mu = 5$$ minutes and a
Comparing Mean Reaction Times Between Two Groups
A psychological study compares reaction times under two conditions. Group A (n = 40) has a mean reac
Confidence Interval and Sampling Distribution in Height Estimation
A researcher aims to estimate the average height of college students with a margin of error of $$1$$
Effect of New Teaching Method on Student Scores
A school district is testing a new teaching method. Two groups of students are studied: a control gr
Effect of Restaurant Remodel on Customer Behavior
A fast-food restaurant tested whether remodeling their premises had an effect on how much food custo
Employment Benefits Perception
A company surveyed its employees regarding their perception of employment benefits. The responses ar
Environmental Concerns by Community Type
A survey was conducted to assess environmental concerns among residents in different community types
Evaluating Sample Proportions in a Survey
A campus dining satisfaction survey indicates that 70% of all students are satisfied with the dining
Financial Returns: Biased vs. Unbiased Estimators
Investment analysts use two estimators to predict the expected return of a financial asset. Estimato
Genetic Mutations in New Fathers
A study estimates that 40-year-old men contribute an average of $$65$$ genetic mutations (with a sta
Hospital Patient Satisfaction by Department
A hospital surveyed patient satisfaction in three departments. The table below displays the number o
Lightbulb Life Expectancy Analysis
A particular brand of lightbulb has a lifespan that is approximately normally distributed with a mea
Lightbulb Life Expectancy Analysis
A certain brand of lightbulbs has a life expectancy that is approximately normally distributed with
Naked Mole Rat Life Expectancy Study
Naked mole rats have a life expectancy that is approximately normally distributed with a mean of $$2
Quality Control in Manufacturing: CLT Application
A manufacturing plant produces metal rods whose lengths are not normally distributed, but have a pop
Sampling Distribution for Sample Means: Caffeine Content in Energy Drinks
An energy drink has its caffeine content normally distributed with a mean of $$\mu = 200$$ mg and a
Sampling Distribution for Sample Means: Energy Drink Caffeine Levels
An energy drink has an average caffeine content of $$\mu = 200$$ mg with a standard deviation of $$\
Sampling Distribution for Sample Proportions in Math Anxiety Study
A recent study estimates that 80% of people with high math anxiety experience brain activity similar
Simulation and Empirical Distribution: Study Habits
A researcher collects data on weekly study hours for high school students. In an initial sample of 1
Sports Performance Data Analysis - Batting Averages
In a baseball league, the average batting average is 0.280 with a standard deviation of 0.030. A coa
Student Performance and Study Techniques
A study compared two study methods: using flashcards versus summarization. In the flashcards group (
Widget Lifespan Quality Control
A factory produces widgets with an average lifespan of $$500$$ hours and a standard deviation of $$2
Advertising Impact on Brand Recognition
A company launched an advertising campaign in two regions. In Region 1, a post-campaign survey of 50
Analysis of Survey Data on Online Learning
A survey of 150 students indicates that 90 prefer online learning. A table summarizing the responses
Coffee Shop Loyalty
A coffee shop chain is investigating customer loyalty. A survey at the downtown branch (Group A) sam
Comparing Defect Rates in Two Factories
Two factories, Factory A and Factory B, manufacture the same electronic component. A quality control
Comparing Satisfaction Between Two Stores
A retail chain wants to compare customer satisfaction between two of its stores. In Store A, 150 cus
Customer Preference Difference Between Cities
A regional chain surveys customers in two cities regarding their preference for a new product. In Ci
Customer Satisfaction in a Retail Store
A large retail chain conducted a survey to measure customer satisfaction. Out of a simple random sam
Diet Choices by Gender
A survey was conducted to analyze diet choices among male and female participants. Participants were
Epidemiology Study: Difference in Disease Incidence
An epidemiological study examines disease incidence in two groups. In the exposed group (n = 400), t
Evaluating Strike Support
A union conducted a survey among 125 members to decide on whether to support a strike. In the survey
Factory Quality Control Analysis
In a factory, quality control is carried out by inspecting a sample of items. Out of 800 items inspe
Government Policy Approval Confidence Interval
A polling organization surveyed 800 voters to measure the approval of a recent government policy. Am
Hypothesis Testing for Brand Satisfaction
A company claims that 85% of its consumers are satisfied with its product. A random survey of 200 cu
Interpreting a Confidence Interval
A study on dietary habits produces a 95% confidence interval for the proportion of adults consuming
Job Satisfaction by Shift Work
A hospital survey examined job satisfaction among nurses working on the Day Shift and the Night Shif
Medical Trial: Comparing Treatment and Control
A clinical trial compares the effectiveness of a new treatment with a placebo. In the treatment grou
Online Education Satisfaction
A study comparing satisfaction with education methods surveyed two groups. One group of online stude
Political Campaign Support Analysis
A political campaign conducted a survey to determine support for a candidate. In the survey, a simpl
Political Opinion Poll Analysis
A political poll was conducted to assess support for a proposed tax bill. In a simple random sample
Political Polling: Candidate Approval
Two independent polls were conducted to assess approval ratings for a political candidate. Poll 1, s
Public Library Usage Survey
A city council conducted a survey to determine the proportion of residents using the public library.
Research on Smoking Cessation Program
A study is conducted on a smoking cessation program to estimate the proportion of participants who s
Simulation and Analysis for Rare Diseases
An epidemiologist is studying a rare disease with an estimated prevalence of 0.5%. They simulate dra
Smartphone Brand Preference by Income Level
A market research survey categorized respondents by income level and their preferred smartphone bran
Social Media Campaign Engagement Analysis
A company runs a social media campaign aiming for a target engagement rate of 40%. In a sample of 60
Social Media Influence Study
A marketing firm is investigating whether exposure to a popular social media influencer affects the
Testing for Change in Voter Intent Over Time
An exit poll conducted before and after a major debate shows different levels of support for Candida
University Enrollment Statistics
A university collected enrollment data to compare the study mode (Full-time vs. Part-time) of Domest
University Policy Support Analysis
A university claims that 60% of its students support a proposed policy change. A random sample of 20
Urban vs. Rural: Survey on Public Transportation Usage
A survey was conducted to compare the use of public transportation between urban and rural residents
Website A/B Testing
An online retailer is testing two versions of its webpage (Version A and Version B) to determine whi
Advertising Budget and Sales Performance Analysis
The scatterplot below represents data on a company's monthly advertising budget (in thousands of dol
Analysis of Weekly Exercise Duration
A wellness program is designed to increase weekly exercise time. In a sample of 16 participants unde
Change in Manufacturing Process: Product Lifespan
A manufacturing company claims that a new manufacturing process increases the lifespan of its produc
Comparing New Drug Efficacy
A pharmaceutical study compares two medications for lowering blood pressure. Group 1 (Drug A) consis
Comparing Two Diets
A nutritionist compares the effects of two diets on weight loss. In a study, Diet 1 (n = 30) results
Customer Satisfaction at Two Store Branches
A retail chain collects customer satisfaction ratings (on a scale of 1 to 10) from two store branche
Customer Satisfaction Survey
A popular online retailer claims an average customer satisfaction rating of 8.5 (on a 10-point scale
Daily Steps: Wearable Device Analysis
A fitness tracker company wishes to estimate the average number of steps taken per day by its users.
Delivery Times: Standard vs. Express Shipping
A logistics company wants to compare the average delivery times for its two shipping methods. Data c
Detection of Production Process Anomalies via Simulation
A factory monitors its production process by measuring the deviation from a target product dimension
Effectiveness of a New Drug
A clinical trial was conducted to determine if a new drug reduces systolic blood pressure. For each
Effectiveness of Drug Treatments
A clinical trial compares two drug treatments (Drug X and Drug Y) for a certain condition. Patients
Election Polling Power Analysis
In an election poll, a candidate claims to have 70% support. A critic believes the true support is 6
Employee Productivity Analysis
A study compares employee productivity scores between two departments. Department 1 (n = 30) has a s
Employee Training Effectiveness
A company conducts a study to evaluate the effectiveness of a new training program. The program's im
Evaluating a Mobile App's Impact on Daily Step Count
A health technology firm develops a new mobile application aimed at increasing daily physical activi
Examining Teaching Methods
A school is comparing two teaching methods: Traditional and Modern. Student outcomes are classified
Fuel Consumption and Distance Traveled Analysis
The scatterplot below displays data on the gallons of fuel used (x-axis) and the corresponding dista
Impact of New Traffic Signals on Commute Times
A city installs new traffic signals at a busy intersection to improve traffic flow. Traffic engineer
Life Span Analysis of Light Bulbs
A manufacturer claims that its light bulbs have a long lifespan. In a quality test of 15 randomly se
Lifespan of New Light Bulbs
A company tests the lifespan of a new type of light bulb. A random sample of 18 bulbs shows a mean l
Medical Device Response Time Analysis
A study is carried out to evaluate the response time (in seconds) of a new medical device. A random
New Coffee Blend and Alertness Test
A beverage company is testing whether a new coffee blend improves alertness by reducing reaction tim
Plant Growth under Different Fertilizers
A botanist is studying the effect of a new fertilizer on plant growth. A random sample of 12 plants
Reaction Time Hypothesis Test
A psychologist wishes to test a manufacturer's claim that the average driver reaction time is \(0.8\
SAT Preparation Class Improvement
A tutor runs an SAT preparation class with 25 students. The differences between the post-test and pr
Simulation from a Bimodal Population
A researcher is studying a population that exhibits a bimodal distribution (e.g., test scores from t
Simulation of Sampling Distribution for Average Household Income
An economist is studying household incomes, which are known to be right-skewed. The economist uses s
Simulation of Sampling Distribution of Mean Reaction Times
In a cognitive psychology study, reaction times (in milliseconds) to a stimulus are collected. A sim
Social Media Usage Before and After an Intervention
A researcher studies the effect of a digital detox program on daily hours spent on social media. For
Weight Loss Confidence Interval
A nutritionist is studying the effectiveness of a new weight loss program. A random sample of 20 par
Weight Reduction Program Evaluation
A fitness center evaluates its new weight reduction program by measuring the weights of 15 participa
Wind Speed Measurements: Station Upgrade Impact
A weather station upgrades its sensors and collects paired wind speed measurements from before and a
Animal Species Distribution in Habitats: Chi-Square Test
Researchers collected counts of three animal species (Deer, Rabbit, Fox) in two habitats. The counts
Customer Satisfaction Ratings Across Service Centers
Data has been collected from three service centers regarding customer satisfaction. The centers reco
Diet Preference Among Athletes
In a study, three groups of athletes (Football, Basketball, Soccer) were surveyed regarding their di
Drinking Habits and Health Outcomes: Test for Independence
A health study surveys 300 individuals, recording their drinking habits (Never, Occasionally, Regula
Drug Side Effects Analysis: Chi-Square Test for Independence
In a controlled clinical trial, researchers are investigating whether the frequency of certain side
Education Level and Internet Usage Frequency – Chi-Square Test for Independence
A survey of 500 individuals collected data on their education level (High School, Bachelor's, Master
Effectiveness of a New Training Program across Branches
A company implements a new training program in three of its branches. After the program, employees a
Election Polls: Goodness-of-Fit for Candidate Support Ratios
In a local election survey of 500 voters, the observed support percentages for candidates were: Cand
Evaluating Student Performance: Chi-Square Goodness-of-Fit in Grades Distribution
A large high school believes that the distribution of final letter grades (A, B, C, D, F) on a stand
Fair Dice Rolling Goodness-of-Fit Test
A die is believed to be fair. In 120 rolls, the outcomes were observed as follows: Face 1 = 14, Face
FRQ 1: Distribution of Customer Preference for a New Snack
A snack company claims that the preferences for flavors of its new snack follow the proportions: Fla
FRQ 2: Association Between Smoking Behavior and Gender
A public health survey collected data on smoking status and gender from 150 individuals. The observe
FRQ 3: Voter Preferences by Age Group: A Homogeneity Test
A study categorizes voters into three age groups (Young, Middle, Older) and records whether they sup
FRQ 8: Sports Participation and Academic Performance
A school investigates whether participation in sports is associated with academic performance. The f
FRQ 9: Student Enrollment Preferences Across Tracks
A high school offers four different tracks: STEM, Humanities, Arts, and Vocational. The school expec
FRQ 12: Employee Training Program and Job Promotion
A company is investigating the effectiveness of its training program on job promotions. The collecte
Genetics Research: Rat Coat Colors
In a genetics experiment, the expected Mendelian ratio for rat coat colors is 3:1 (dominant: recessi
Goodness-of-Fit Test for Web Traffic Sources
A website manager expects that web traffic comes from four sources with the following proportions: D
Independence of Smoking and Lung Disease
A public health survey collected data from 300 participants to investigate the relationship between
Production Line Defect Rates Homogeneity Test
A factory operates four production lines, each producing a sample of 200 items. The numbers of defec
Quality Control Across Production Lines – Chi-Square Test for Homogeneity
A company monitors the quality of items produced by three production lines. In monthly samples of 15
Race Participation in Marathon
A marathon organizer expects the racial participation to follow these percentages: Group 1 = 30%, Gr
Shopping Behavior: Online vs. In-store by Age Group
Researchers want to examine if shopping mode (Online vs. In-store) is related to age group. The surv
Smartphone Brand Market Share: Goodness-of-Fit Test
A survey of 200 smartphone users records their preferred brand among four brands: A, B, C, and D. Th
Social Media Platform Usage
A marketing agency expects that among 500 consumers, the usage of social media platforms is distribu
Teacher Satisfaction by Department: Chi-Square Test for Homogeneity
A school district wishes to determine if job satisfaction among teachers varies by department (Math,
Teaching Methods Effectiveness: Homogeneity Test
An educational study compares the effectiveness of three teaching methods (Method 1, Method 2, Metho
Traffic Light Malfunction Analysis
A city’s transportation department monitors traffic light performance. They expect that 90% of signa
Transportation Mode Among City Residents
A city survey examines the relationship between type of residence (Urban vs. Suburban) and preferred
Type of Transportation and Commute Satisfaction
A survey of 530 commuters collected data on their primary mode of transportation (Car, Bus, Bike, Wa
Advertising Budget and Sales Revenue
A marketing analyst is studying the relationship between a company’s monthly advertising budget (in
Advertising Spend and Website Traffic
A company analyzed how its weekly advertising spend (in thousands of dollars) influences website tra
Agricultural Yield Analysis
Agricultural scientists examine the effect of fertilizer application (in kg/ha) on crop yield (in to
Air Quality and Traffic Flow
A study investigates whether daily traffic flow (vehicles per hour) is associated with urban air pol
Biking Speed and Heart Rate
A sports scientist is investigating the relationship between average biking speed (in mph) during ex
Coffee Consumption and Alertness
Researchers are investigating the relationship between the number of cups of coffee consumed per day
Coffee Consumption and Alertness
A researcher investigated the relationship between daily coffee consumption (measured in cups) and a
Coffee Consumption and Anxiety Levels
A psychologist investigates whether there is a relationship between the number of cups of coffee con
Crop Yield and Fertilizer Application
An agronomist is examining how the amount of fertilizer applied (x, in kg) affects crop yield (y, in
Effect of Class Size on Student Achievement
An education researcher examines data from 50 classrooms to study the relationship between class siz
Effects of Weather on Tourist Visits
The city tourism board collected data to study the relationship between daily high temperature (in °
Electricity Bill vs Temperature
A utility company studied the relationship between the average monthly temperature (in $$^\circ F$$)
Engine Size vs Highway Fuel Efficiency
An automobile researcher is studying the relationship between engine size (in liters) and highway fu
Engine Temperature and Efficiency Loss
An engineering study investigates the effect of engine temperature ($$x$$, in $$^\circ C$$) on effic
Engineering: Stress and Strain in Alloys
In an experiment studying a new alloy, engineers measured stress (x, in MPa) and strain (y, dimensio
Environmental Study: Pollutant Concentration and Respiratory Issue Rates
Researchers are studying the impact of pollutant concentration (in parts per million, ppm) on the ra
Impact of Workout Hours on Body Fat Percentage
A fitness study collected data on the number of hours individuals work out per week (x) and their bo
Modeling Blood Pressure Response to Medication Dosage
A medical study investigates the effect of medication dosage (x, in mg) on the reduction in systolic
Practice Time and Music Performance Skill
A study investigates the effect of weekly practice hours ($$x$$) on a music performance skill score
Predicting Sales Based on Advertising Budget
A company wants to understand the relationship between its advertising spending (in thousands of dol
Predicting Student Performance with Attendance Rates
A teacher collects data on student attendance rates (x, in percentage) and corresponding performance
Rainfall and Crop Yield
An agricultural study investigates the relationship between total rainfall (in inches) during the gr
Reaction Rate in Chemistry: Temperature and Reaction Time
An experiment investigates the effect of temperature (x, in °C) on reaction time (y, in seconds). Da
Relationship Between Stress Level and Reaction Time
A psychological experiment collected data on stress levels (x, on a scale of 0-100) and reaction tim
Sleep Hours and Cognitive Performance
A study examines the effect of sleep hours (x) on cognitive performance (y, measured as a test score
Social Media Advertising and Customer Clicks
A digital marketer investigates the relationship between social media advertising spending (x, in th
Social Media Influence on Product Sales Simulation
A business analyst wants to understand the effect of time spent on social media advertising (in hour
Speed and Fuel Efficiency
A study examines the relationship between vehicle speed ($$x$$, in mph) and fuel efficiency ($$y$$,
Student Performance and Attendance
A school administrator wants to understand the relationship between class attendance and test scores
Student Study Hours and Exam Scores Simulation
A high school teacher is interested in how the number of hours spent studying affects exam scores. T
Temperature Effect on Ice Cream Sales
An ice cream vendor recorded daily temperature (in °F) and daily ice cream sales (in dollars) over 3
Weight Loss and Diet Adherence
A nutritionist is studying the relationship between the number of diet counseling sessions attended
Everyone is relying on Knowt, and we never let them down.
We have over 5 million resources across various exams, and subjects to refer to at any point.
We’ve found the best flashcards & notes on Knowt.