AP Statistics FRQ Room

Advertising Campaigns and New Customer Sign-ups

A company ran two advertising campaigns to increase new customer sign-ups. In Campaign 1, there were

Charitable Donation Timing by Age Group

A charity collected data on donation timings (Morning, Afternoon, Evening) and donor age group (Youn

Community Exercise Program and Blood Pressure Reduction

A public health study is conducted to evaluate the effectiveness of a community exercise program on

Daily Caloric Intake Data Analysis

A nutrition study collected data on the daily caloric intake of 170 individuals. The results, broken

Dietary Preferences by Gender

A survey collected responses from 270 individuals regarding their dietary preference (Vegetarian, No

Effect of a Multiplicative Transformation on Distance Data

A group of athletes has their running distances (in kilometers) recorded as: {5, 6, 8, 7, 10, 9}. Th

Effect of Fertilizer Types on Tomato Yield

An agricultural experiment is designed to test whether different types of fertilizer affect tomato y

Effect of Outliers on the Sampling Distribution of the Mean

Consider two populations of student test scores. Population A does not contain extreme scores while

Effects of Adding a Constant on Measures of Spread

Consider the dataset of exam scores: {65, 70, 75, 80, 85}. Answer the following:

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

Evaluating Marketing Strategies: Online Ad A/B Test

A company performed an A/B test for two versions of an online advertisement to compare their click-t

Examining Non-Response Bias in Mail Surveys

Two separate mail surveys were conducted in different regions. In Region X, 150 out of 300 surveys w

Home Run Distances Analysis

Consider the following set of home run distances (in feet) measured at 13 ballparks: $$\{387, 400,

Impact of Study Methods on Exam Performance

A school district plans a study to determine whether group study or individual study leads to higher

Internet Usage Among College Students

A survey of 220 college students recorded the number of hours they spend online per day. The results

Investigating Class Test Scores

A teacher collected the following test scores from a class: {55, 60, 62, 68, 70, 72, 75, 78, 80, 83,

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

Irrigation Techniques and Crop Yield

An agricultural study is set up to compare three irrigation techniques (drip, sprinkler, and flood)

Online Retail Customer Spending Analysis

An online retail store collects data on customer spending. In a sample of 60 customers, the mean spe

Parent Survey on School Length

A survey of 2000 parents asked which school year length they preferred. The following table summariz

Phone App Usage Times

Daily phone app usage is normally distributed with a mean of $$120$$ minutes and a standard deviatio

Regression Analysis: Height and Shoe Size in Adolescents

A study on adolescents collected data on height (in cm) and shoe size. The least-squares regression

Sampling Distribution of Average Purchase Amount

Individual consumer purchase amounts are normally distributed with a mean of $$50$$ dollars and a st

Simulated Sampling Distribution of the Range from a Uniform Distribution

Consider a population with a uniform distribution on the interval [0, 1]. A simulation is performed

Simulated Sampling Distribution of the Standard Deviation

Consider a normal population with $$\mu = 50$$ and $$\sigma = 8$$. A researcher uses simulation to g

Sleep Deprivation and Reaction Times

A behavioral study is designed to examine the effect of sleep deprivation on reaction times. Partici

Social Media Usage and Employee Productivity

A business is interested in evaluating whether limiting social media usage during work hours increas

Analyzing Temperature Effects on Electricity Consumption

A utility company collected data on average daily temperature (in °F) and electricity consumption (i

Assessing the Sampling Distribution of Predicted Values in Linear Regression via Simulation

In a study examining the relationship between advertising expenditure (x) and sales (y), a simulatio

Athletic Performance Correlation Analysis

A study on athletes observed the relationship between hours of training per week (x) and competition

Bootstrap Simulation for the Regression Intercept's Sampling Distribution

A data analyst uses the bootstrap method to approximate the sampling distribution of the regression

Call Center Quick Resolutions

At a call center, the probability that a call is resolved within 3 minutes is $$0.2$$. Let $$Y$$ rep

Chi-Square Analysis for Dietary Habits and Exercise Frequency

A nutrition study classifies 300 individuals by their dietary habit (Vegetarian, Non-Vegetarian) and

Comparing Effectiveness of Educational Workshops

An educational organization wants to compare the effectiveness of two types of workshops: traditiona

Comparing Two Regression Models for Chlorophyll Content Prediction

A biologist is studying the relationship between light intensity (x) and chlorophyll content in leav

Computing Regression Statistics from Summary Data: Advertising and Sales

A market research study investigates the relationship between advertising expenditure (X, in thousan

Constructing a Contingency Table from Raw Data

A researcher surveying 100 individuals collected the following raw counts regarding gender (Male, Fe

Contingency Table Analysis: Cuteness Factor Study

In a study on the Cuteness Factor, 250 volunteers were shown pictures from three categories: Cute An

Correlation and Coefficient of Determination in Exam Performance

A researcher studying exam performance collected data on the number of hours students studied (X) an

Elderly Health Program Evaluation

An evaluation was carried out to assess whether participation in a health program by elderly individ

Highway Traffic Flow and Accident Rates

A study examined 25 highways to investigate the relationship between average daily traffic flow (x,

Housing Prices and Home Size

A study of 40 houses produced the regression equation $$\hat{y}=50+0.15x$$ predicting house price (i

Housing Prices and Square Footage Analysis

A real estate analyst collected data on various houses regarding their square footage (in square fee

Impact of Caffeine Intake on Reaction Time

In a laboratory study, researchers measured participants' reaction times (in seconds) after ingestin

Interpreting the Sign and Magnitude of the Correlation Coefficient

A study examining the relationship between daily temperature (X) and ice cream sales (Y) finds a cor

Marketing Survey: Advertising Budget vs. New Customers

A marketing survey collected data on weekly advertising budget (x, in thousands of dollars) and the

Movie Genre Preference and Age Group

A survey of 200 moviegoers was conducted to investigate the relationship between movie genre prefere

Museum Visits and Visitor Satisfaction

A local museum surveyed 40 visitors about the number of times they visited the museum in the past ye

Pharmaceutical Dosage Testing

A pharmaceutical company produces tablets designed to contain an active ingredient with a prescribed

Political Polling: Approval Ratings

A polling organization is studying the approval ratings of a political leader among urban and rural

Predicting Student Exam Scores from Study Hours

A researcher investigates the relationship between the number of hours a student studies (x) and the

Promotion Program Success Comparison

A company implemented two distinct promotional programs to boost sales. In Program 1, 92 out of 150

Quality Control in a Bakery

A bakery finds that historically 2% of its cookies are too hard. In a sample of $$100$$ cookies, let

Regression Analysis of Movie Attendance and Concession Sales

A movie theater records daily attendance (x) and the number of concession sales (y, measured in hund

Restaurant Order Survey

A restaurant surveyed 140 customers to see if there was any association between meal type (Vegetaria

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

Simulation of the Sampling Distribution of a Cell Proportion in a Contingency Table

A study gathers categorical data in a two-way table regarding customer satisfaction (Satisfied/Not S

Simulation Study of the Sampling Distribution of the Correlation Coefficient

Researchers are interested in studying the correlation between two variables, X and Y. To assess the

Social Media Engagement Analysis

A study examines the relationship between the number of posts an individual makes per day (x) and th

Website A/B Testing for Click-Through Rates

A technology company is testing two versions of its website (Version A and Version B) to see which o

Website Click-Through Rate

An online advertisement has a click-through probability of $$0.15$$ for each visitor. Suppose that 5

Academic Performance: Hours Studied and Test Scores

In a high school, a teacher investigates the relationship between the number of hours students study

Analysis of Recycling Behavior

A survey was conducted to study recycling habits among individuals with different education levels.

Cluster Sampling in Educational Research

A school district administrator wants to assess students' attitudes toward a new curriculum. To redu

Cluster Sampling in Educational Testing

A school district with 50 schools wants to evaluate a new teaching method. They decide to randomly s

Comparing Test Scores Between Two Teaching Methods

A school is evaluating two different teaching methods. Group A, using Teaching Method A, had 25 stud

Customer Feedback for a New Product

A technology company collected customer feedback regarding a new product via two purchasing channels

Customer Service Feedback

A company collected customer service feedback from three channels: Online, In-store, and Phone. The

Designing a Double-Blind Experiment for a New Drug

A pharmaceutical company intends to test a new drug aimed at reducing blood pressure. To eliminate b

Designing a Prospective Study for Teaching Methods

A school district wants to study the effect of a new teaching method on student performance on stand

Effect of Noise Levels on Sleep Quality

An environmental study investigates the association between ambient noise level (in decibels, x) and

Effect of Outliers on Sampling Distributions

In statistical analysis, outliers can notably influence the results of a study. Answer the following

Estimating Average Park Visit Duration

A study is conducted to assess the average length of time (in minutes) that visitors spend at a loca

Evaluating the Effect of Exercise on Blood Pressure Reduction

A study measured the reduction in blood pressure in two groups over a 6‐month period. Group 1 (Exerc

Evaluating the Sampling Frame in an Urban Survey

A research team plans to survey residents of a large urban area on community services. They initiall

Exploring Stratified Sampling and its Sampling Distribution via Simulation

A researcher is studying a population that is divided into two distinct strata with different means.

Flu Vaccination Campaign and Illness Spread

A hospital is reviewing its flu vaccination campaign by comparing the incidence of flu among vaccina

Heart Rate Recovery and Fitness Level

In a cardiovascular fitness study, researchers examine if higher fitness levels (measured by a fitne

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 Product Purchase

A company conducted a study on the effect of different advertisement types (Online, TV, Print) on pr

Investigating Effects of Population Variability on Sampling Distributions

Two populations have the same mean $$\mu = 100$$ but different standard deviations: $$\sigma_1 = 10$

Investigating Response Time in Emergency Calls

A retrospective study collected data on the response times (in minutes) of emergency services from 6

Investigating Sampling Bias in a Voluntary Response Survey on Social Media Usage

A market research firm conducts an online survey where participants voluntarily respond to questions

Music Therapy and Stress Levels

A study is designed to test whether music therapy can reduce stress levels in adults. A double-blind

Quality Control in Manufacturing

A manufacturing process produces items, each with a 2% chance of being defective. A quality control

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

Retail Store Checkout Efficiency Study

A study compared the average waiting time at checkout between two methods in a retail store. For the

Salesperson Success: Geometric Probability

A salesperson meets potential customers, and the probability of making a sale during any meeting is

Simulating the Sampling Distribution from a Skewed Distribution

A fast food restaurant is interested in the waiting times (in minutes) of its customers, which are p

Smartphone Usage and Sleep Quality

Examine the relationship between smartphone usage and sleep quality among college students. Research

Systematic Sampling Implementation

A researcher intends to select 150 students from a high school of 1500 students using systematic sam

Traffic Flow System and Commuting Times

A city is testing a new traffic flow system designed to reduce commuting times during rush hour. The

Voting Patterns in a Retrospective Study

A retrospective study collected exit poll data to determine the level of support for Policy X among

Advertising Budget and Sales Regression Analysis

A company investigates the relationship between its advertising spending (in thousand dollars) and i

Coffee Shop Latte Prices

A national coffee shop chain wants to estimate the average price of lattes across its stores. A rand

Comparing Customer Satisfaction in Two Coffee Shops

A survey was conducted to compare customer satisfaction between two coffee shops. The table below su

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 Patient Wait Times at Two Clinics

Two clinics recorded patient wait times. Clinic 1 (n = 40) had an average wait time of 25 minutes wi

Cumulative Probability Distribution in AP Exam Scores

The following table shows the distribution of scores on an AP exam: | Score | Frequency | |-------|

Customer Satisfaction Survey on New Service Protocol

A company is testing a new customer service protocol to improve satisfaction. Customers are randomly

Defective Products in Quality Control (Binomial Distribution)

In a quality control process, each product has a defect probability of 0.08 and is inspected indepen

Effect of Fertilizer Type on Plant Growth

An agricultural researcher is studying the effects of three different fertilizer types on plant grow

Employee Training and Department Performance

A company recorded the outcomes of a recent employee training program across three departments. The

Energy Consumption Random Variables

In a small town, the daily household energy consumption (in kWh) is modeled by the following distrib

Exam Score Cumulative Distribution

The following table displays the distribution of scores on an exam from 200 students:

Fuel Efficiency Comparison between Two Vehicle Models

An automotive study compared the fuel efficiency of two car models. Model X was tested on 30 cars, y

Household Income and Entertainment Expenditure Regression Analysis

A survey of households examines the relationship between monthly income (in dollars) and monthly spe

Impact of Social Media Usage on Academic Performance

A study is conducted to examine the relationship between time spent on social media and academic per

Investigative Study on Public Health Intervention

A local government is assessing the effectiveness of a new public health campaign aimed at reducing

Mobile App Daily Engagement

A mobile app developer claims that at least 40% of users engage daily with the app. In a random samp

Multistage Probability: Virus Infection on Campus Computers

On a university campus, 60% of computers run Windows, 30% run Apple, and 10% run Linux. A virus affe

Political Polling: Voting Intentions by Age Group

A polling agency surveyed 300 voters about their intention to vote 'Yes' or 'No' on a particular iss

Quality Control in Manufacturing

A factory produces widgets, each having an independent 5% chance of being defective. Quality control

Retail Customer Purchases: Random Variable Analysis

A survey at a retail store reveals that the number of items purchased per visit follows this distrib

Sales Calls Geometric Distribution

A salesperson makes calls until she gets her first sale. The probability of getting a sale on any gi

Scatterplot Regression Analysis on Study Habits

A researcher collects data on the number of hours students study (x) and their exam scores (y). The

Simulated Distribution of Sample Proportions with a Biased Coin

A simulation uses a biased coin with a probability of heads $$p = 0.8$$. In each simulation run, the

Simulating Clinical Trial Successes

A new drug has a success probability of 0.65. In a clinical trial, 30 patients are treated independe

Testing a New App Feature through A/B Testing

A tech company is conducting an A/B test to evaluate a new feature that is intended to enhance user

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

Transportation and Work Patterns Survey

A survey of 500 people recorded their preferred mode of transportation and work location (Remote or

Website Conversion Rates: A/B Testing

An online retailer is testing two different webpage designs. Landing Page A received 120 conversions

Website Navigation and Conversion Rates

A website conducted an A/B test with two versions (A and B) and recorded visitor conversion outcomes

Website Redesign and Sales Conversion Rates

A company tested its website performance before and after a redesign. The old design resulted in 90

Analyzing Differences in Means Between Two Machines

Two machines produce metal rods. Machine A produces rods with a mean length of $$20$$ cm and a stand

Battery Lifespan Analysis

A company produces batteries whose lifespans (in hours) are normally distributed with $$\mu = 500$$

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 $$1$$

Customer Complaints by Service Type

A telecommunications company recorded customer complaints for two types of services: Phone Service a

Difference in Sample Proportions: Revamped vs. Unrevamped Restaurant

A study compares customer behavior at two restaurants. At a revamped restaurant, 30% of a sample of

Differences in Daily Step Count due to Wellness Program

A company introduced a wellness program and wants to assess its impact on daily step counts among it

Estimator Evaluation in Baseball Manufacturing

In a quality control study for manufacturing professional baseballs (true mean weight = $$146$$ gram

Evaluating Estimators for Baseball Weight

A quality control department is evaluating five different statistical estimators to measure the weig

Evaluating Genetic Mutations in New Fathers

A study examines the number of genetic mutations passed on by new fathers of different ages. It is e

LED Lightbulb Lifespan Probability Analysis

A manufacturer produces LED lightbulbs whose lifespans are normally distributed with a mean of $$\mu

Lightbulb Lifespan Probabilities

A certain brand of lightbulbs has a lifespan that is normally distributed with mean $$\mu = 1500$$ h

Math Anxiety Brain Activity Proportions

It is estimated that $$80\%$$ of individuals with high math anxiety exhibit brain activity similar t

Movie Theater Attendance by Genre Preference

A movie theater analyzed attendance frequency based on movie genre preference. The table below categ

Music Streaming Service Satisfaction

A music streaming service is comparing satisfaction levels between Free and Premium subscription use

Psychological Test Reliability

A psychological assessment is administered to a random sample of $$50$$ individuals. The test has a

Sample Proportion Variability in Customer Preference Studies

Two separate studies examine customer preference for a new product. Study 1 finds 60% preference in

Sample Variance Distribution in Produce Weights

A study measures the weights of produce, where the population variance is known to be $$16$$ (kg^2).

Sampling Distribution for Differences in Sample Proportions in Political Polling

In a political poll, two districts are surveyed. In District A, 60% of 500 voters support a policy,

Sampling Distribution of the Maximum: Weather Temperature Extremes

A climatologist is studying daily maximum temperatures in a city. The theoretical population maximum

Simulated Sampling Distribution for Eco-Friendly Vehicle Mileage

An automobile manufacturer tests its eco-friendly vehicles whose fuel efficiency (in miles per gallo

Simulation of Sampling Distributions: Dreams Recorded

A study finds that high school students remember an average of 3.4 dreams per night with a variance

Using invNorm in Sampling Distributions: Statistical Thresholds

Scores on a standardized test are normally distributed with a mean of $$\mu = 500$$ and a standard d

Voting Behavior by Gender

A political study analyzed voting behavior based on gender. The table below displays the counts of m

Analyzing Proportions as a Function of Batch Size

A manufacturing researcher is investigating the relationship between the size of a production batch

Assessing Advertising Effectiveness with Proportion Data

An advertising firm claims that its new campaign results in a purchase rate of at least 30%. In an e

Comparative Study on Voter Registration Between Two States

Two neighboring states conducted surveys on voter registration. In State A, 320 out of 400 eligible

Comparative Study on Voter Turnout in Urban and Rural Areas

A study was conducted comparing voter turnout in urban and rural areas. In an urban sample of 400 re

Comparing Defect Rates in Two Factories

Two factories, Factory A and Factory B, manufacture the same electronic component. A quality control

Conservation Program Study

A local government has implemented an environmental conservation program intended to increase the pr

Designing a Survey for Voting Behavior

A political researcher plans to estimate the proportion of voters who will support a particular cand

Digital Platform Success Rate Comparison

Two schools use different digital learning platforms. In School X, 90 out of 150 students successful

Effect of an Advertisement on Purchase Intent

A company wishes to evaluate the impact of an advertising campaign on purchase intent. Before the ca

Effectiveness of a Public Health Intervention: Investigative Task

A public health organization is assessing the effectiveness of a new intervention aimed at increasin

Employee Burnout Study

A company conducted a survey to assess employee burnout. In a simple random sample of 250 employees,

Gender Differences in Product Preference

A market survey was conducted to measure interest in a new gadget. A sample of 400 males showed that

Health Study: Smoking Prevalence Comparison

A health study compared the smoking prevalence between two cities. In City A, a sample of 500 respon

Health Survey Confidence Interval Analysis

A local health department conducted a survey regarding residents' compliance with a new health regul

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

Marketing Campaign Response Rate Test

A marketing team asserts that their campaign increases customer engagement, expecting a response rat

Online Shopping Behavior

A survey of customers on an e-commerce website evaluated purchasing behavior across two age groups:

Opinion Poll on Environmental Policy

A survey of 600 citizens was conducted to gauge support for a new environmental policy. Out of the 6

Research on Smoking Cessation Program

A study is conducted on a smoking cessation program to estimate the proportion of participants who s

Sample Size Determination for Desired Margin of Error

A researcher wishes to estimate the proportion of households that recycle with a margin of error of

Satisfaction with Mobile App Features

A tech firm surveys 650 mobile app users and finds that 390 users are satisfied with the app feature

Survey Analysis: Confidence Interval for College Students' Online Class Preference

A survey of college students was conducted to estimate the proportion of students who prefer online

University Enrollment Statistics

A university collected enrollment data to compare the study mode (Full-time vs. Part-time) of Domest

Web Advertisement Click-Through Rates

An online marketing team is comparing the click-through rates of two advertisements. Ad A was shown

Accident Frequency Comparison

An assembly plant records the number of accidents per month in two independent departments over 30 m

Advertising Spend and Website Traffic Analysis

The scatterplot below presents data on monthly advertising spending (in thousands of dollars, x-axis

Battery Lifespan Comparison

Two battery manufacturers are being compared based on the lifespan of their batteries. For Manufactu

Blood Pressure and Sodium Intake Regression

A study investigates the relationship between daily sodium intake (in mg) and systolic blood pressur

Comparing Free-Throw Percentages of Two Basketball Teams

A sports analyst collects data on free-throw percentages of players from two basketball teams. For T

Comparing Teaching Methods via Test Scores

A school is comparing two teaching methods. In a study, 30 students using Method A had an average te

Diet Choice and Energy Levels

A nutritionist investigates whether there is an association between diet type (Vegetarian vs. Omnivo

Effect of Medication on Blood Pressure: Paired Data Analysis

A study was conducted on 30 patients to evaluate the effect of a new medication on systolic blood pr

Effectiveness of Tutoring Program Investigation

A school district is interested in the effectiveness of a new tutoring program on improving student

Evaluating a Sleep Intervention

A fitness center implements a sleep intervention program aimed at increasing the average number of h

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 a Study Technique on SAT Scores

A high school implements a new study technique intended to improve student SAT scores. A group of 40

Impact of Training Programs on Test Scores

An educational study compares the effectiveness of two training programs (Program A and Program B) o

Machine Downtime Analysis

A manufacturing plant monitors the daily downtime (in minutes) of a critical machine. Over 40 indepe

Pre- and Post-Treatment Blood Pressure

A clinical trial is conducted to assess the effectiveness of a new treatment for lowering blood pres

Pre-Test and Post-Test Scores Analysis

The scatterplot below represents data on students' pre-test scores (x-axis) and post-test scores (y-

Response Time in a Virtual Reality Task

A technology company is testing a new virtual reality (VR) system for gaming. They measure the respo

Role of Random Sampling in Simulation Studies

A statistician conducts a simulation study by drawing 1000 random samples of size n = 25 from a data

Student Participation in Extracurricular Activities

Researchers are studying the relationship between club membership and academic achievement in a samp

Testing Mean Daily Water Consumption

A municipal claim states that the mean daily water consumption in a city is 150 liters. A survey of

Weight Reduction Program Evaluation

A fitness center evaluates its new weight reduction program by measuring the weights of 15 participa

Advertising Channels Effectiveness: Homogeneity Test

A company wants to determine if the effectiveness of three advertising channels (TV, Online, Print)

Analysis of Product Defects in a Manufacturing Process

A manufacturing process produces parts that can fall into one of four categories based on defect typ

Association between Exercise Frequency and Diet Type

A survey of 200 college students examines whether there is an association between exercise frequency

Brand Preference Across Age Groups – Chi-Square Test for Homogeneity

A survey was conducted to determine the preferred soft drink brand (Brand X, Brand Y, Brand Z) among

Chi-Square Analysis of Traffic Light Phases

A transportation engineer hypothesizes that the timing of traffic light phases (green, yellow, red)

Comparing Exhibition Attendance Among Different Museums

Three museums host the same exhibition and record attendance in three categories: High, Medium, and

Comparing Preferences for Social Media Platforms Across Age Groups

A survey examines if social media platform preference is associated with age group. The data collect

Customer Satisfaction Ratings Across Service Centers

Data has been collected from three service centers regarding customer satisfaction. The centers reco

Customer Service Feedback in Retail Stores: Homogeneity Test

A retail chain surveys customer feedback from three stores. Feedback is classified as Positive, Neut

Dice Fairness Goodness-of-Fit Test

A game designer claims that a six-sided die is fair, such that each face appears with probability $$

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

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

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 5: Health Supplement Side Effects

A double-blind clinical trial is conducted to compare a new health supplement with a placebo. Partic

FRQ 6: Association Between Diet and Heart Disease Risk

A study investigates whether there is an association between diet type and heart disease risk. The s

FRQ 8: Sports Participation and Academic Performance

A school investigates whether participation in sports is associated with academic performance. The f

FRQ 16: Association Between Marital Status and Voting Behavior

A study examines whether marital status is associated with voting behavior for Party X versus Party

Gender Distribution Across College Departments

A college collects data on faculty gender distributions across three departments. The data are as fo

Independence Test: Health Food Consumption vs. Age Group

A study collected data on whether individuals regularly consume organic foods (Yes/No) across three

Investigative Analysis: Public Health Awareness Survey

A public health department conducts a multi-stage survey to assess health awareness among residents

Library Membership and Age

A library survey examines whether there is an association between age group and type of membership (

Political Party and Environmental Concern

A survey studies the relationship between political party affiliation (Democratic, Republican, Indep

Quality Control in a Factory

A factory has three production lines, each producing 100 items. Quality control involves checking fo

Restaurant Popularity Goodness-of-Fit

A local food festival features four types of cuisines: Italian, Chinese, Indian, and Mexican. Organi

Smoking and Lung Disease: Independence Test

A survey of 300 individuals reports the following counts: Smoker with lung disease = 40, Smoker with

Sports Participation and Gender – Chi-Square Test for Independence

A school conducted a survey to examine the relationship between gender (Male, Female) and participat

Student Enrollment by Gender and Major: Chi-Square Test for Independence

A university is investigating if student major (STEM, Arts, Business) is independent of gender (Male

Testing a Fair Die – Chi-Square Goodness-of-Fit

To determine if a six-sided die is fair, a student rolls it 600 times. Under the assumption of a fai

Traffic Light Malfunction Analysis

A city’s transportation department monitors traffic light performance. They expect that 90% of signa

Voter Registration Distribution

A state expects voter registration to follow the proportions: Democratic 25%, Republican 35%, and In

Advertising Budget and Sales Revenue

A company collected data on weekly advertising expenditure ($$x$$, in thousands of dollars) and corr

Advertising Budget and Sales Revenue

A marketing analyst is studying the relationship between a company’s monthly advertising budget (in

Car Age and Resale Value

A used car dealer is examining the relationship between a car's age (in years) and its resale value

Clinical Trial Dosage-Response Simulation

A medical researcher investigates the relationship between the dosage of a new medication (in mg) an

Coffee Bean Price and Quality Score

A coffee connoisseur collected data on the price per pound of specialty coffee beans (x, in dollars)

Coffee Consumption and Reaction Time Study

A study was conducted to examine the relationship between the number of cups of coffee consumed by c

Commuting Distance and Weekly Fuel Consumption

A transportation study collected data from 40 drivers to analyze the relationship between commuting

Crop Yields and Fertilizer Usage

Agricultural researchers are investigating the effect of fertilizer amount (in kg per hectare) on cr

Daily Steps vs Calorie Burn

A fitness app developer examined the relationship between the number of daily steps and calorie burn

Daily Study Hours and GPA

Researchers are interested in analyzing the relationship between the number of hours students study

Diet Plans and Weight Loss

A nutritionist compares the effectiveness of two diet plans by analyzing weight loss (in pounds) ove

Effect of Study Habits on Exam Scores

Researchers are studying whether the number of extra study sessions (x) is related to improvement in

Employee Performance and Training Hours

A company is assessing employee performance scores (out of 100) based on the number of training hour

Engine Size vs Highway Fuel Efficiency

An automobile researcher is studying the relationship between engine size (in liters) and highway fu

Fish Population and Pollution Levels

Biologists are studying whether increased pollution levels (x, in parts per million) are associated

Internet Speed and Streaming Buffer Time

A technology company studies the relationship between home internet speed (x, in Mbps) and streaming

Relationship Between Exercise Time and Cholesterol

A health study examines the relationship between weekly hours spent exercising (x) and cholesterol l

Relationship Between Hours Studied and Test Scores

A study collects data from 30 students on the number of hours spent studying (x, in hours) and their

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

River Pollution Levels and Industrial Activity

An environmental scientist is investigating whether the level of industrial activity along a river (

Software Development Efficiency: Lines of Code and Bug Count

A software company wants to study whether the number of lines of code written in a project is relate

Study Hours and SAT Scores: Private vs Public

A researcher studied the relationship between study hours (x) and SAT scores (y) among students from

Technology Training and Productivity

A technology company wants to know if the number of training hours (x) influences employee productiv

Temperature Effect on Ice Cream Sales

An ice cream vendor recorded daily temperature (in °F) and daily ice cream sales (in dollars) over 3

Temperature Effects on Motor Speed

An engineer investigates the effect of ambient temperature ($$x$$, in $$^\circ C$$) on motor speed (

Weather Prediction Model: Slope Simulation

A climatologist is using simulation to explore the relationship between time of day (in hours) and t