AP Statistics FRQ Room

Analyzing a Stem-and-Leaf Plot of Weights

A stem-and-leaf plot displays the weights (in kg) of 40 participants in a fitness program as follows

AP Class Enrollment Analysis

In a school, 300 students were surveyed regarding the number of Advanced Placement (AP) courses they

App Usage: Comparing Two Advertising Campaigns

A mobile app company ran two advertising campaigns. In Campaign 1, 400 out of 800 users clicked the

Blood Pressure Analysis in Clinical Trial

A clinical trial studying a new treatment records the blood pressure of 19 patients. The sample has

BMI and Blood Pressure Regression Analysis

A study examines the relationship between body mass index ($$BMI$$) and systolic blood pressure for

College Admissions Test Scores

Test scores for a college admissions exam are approximately normally distributed with a mean of $$50

Comparing Sampling Distributions from Populations with Different Variances

Two independent populations have identical means but different variances: Population X has $$\sigma^

Cumulative Frequency Analysis: Graduation Ages

A cumulative frequency graph of graduation ages is provided. From the graph, it is observed that the

Customer Satisfaction in Retail Chain

A retail chain surveyed 250 customers regarding their satisfaction level (Satisfied, Neutral, Dissat

Dietary Preferences by Gender

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

Dotplot Representation of Home Run Distances

A dotplot displays the following frequencies for home run distances (in feet): • 387 appears once •

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

Exam Scores: Descriptive Statistics

A teacher collected the scores from a recent exam. The data are summarized in the frequency table be

Exploring Daily Sales Data Using a Stem-and-Leaf Plot

A small business has recorded its daily sales (in dollars) over 15 days. The data are summarized in

Hospital Wait Time

In an emergency room (ER), patient wait times in minutes are normally distributed with a mean of $$4

Impact of Transformations on Data

Consider the following dataset representing test scores: {70, 80, 85, 90, 100}. Answer the followin

Machine Reliability Testing

A machine is tested repeatedly for failure. The probability that the machine fails on any given test

Movie Theater Attendance

Ticket sales at a movie theater are assumed to be normally distributed with a mean of $$150$$ seats

New York City Taxi Mileage Distribution

Taxicabs in New York City are driven an average of 75,000 miles per year with a standard deviation o

Political Polling: Candidate Preference

In a political poll, two states were surveyed to determine the proportion of voters favoring Candida

Product Length Variability in Manufacturing

A manufacturing process produces items with lengths (in centimeters) distributed as shown in the fre

Quality Control in Manufacturing

A quality control inspector examines items on an assembly line. Each item has a 2% chance of being d

School Survey on Categorical Preferences

A high school conducted a survey of 400 students regarding their preferred school day length. The re

Simulation and Transformation Effects on the Sampling Distribution

A researcher studying bacterial growth rates, which follow an exponential distribution, collects dat

Simulation to Construct the Sampling Distribution of the 25th Percentile

An athletic coach is interested in the lower 25th percentile (first quartile) of sprint times (in se

Survey of Preferred Exercise Modalities

A fitness survey of 300 participants asked about their preferred type of exercise. The summary of re

Vehicle Type and Fuel Preference

A survey was conducted among 350 respondents regarding their vehicle type (Car, Truck) and fuel pref

Water Filtration Systems and Water Quality

A city planning department is studying the impact of different water filtration systems on the quali

Z-Scores and Percentile Ranks in a Test Examination

Assume that the scores on a standardized test are normally distributed with a mean of $$80$$ and a s

Advertising Campaign and Sales Analysis

A company tracked the number of social media impressions (in thousands, x) and corresponding product

Advertising Spend and Website Traffic

A small business used data from 15 weeks to analyze the effect of advertising spend on website visit

Art Exposure and Creativity Scores

A survey of 40 art students collected data on the number of hours per week they attend art exhibits

Assessing a New Drug's Efficacy

A clinical trial was conducted to determine the effect of a new drug's dosage (x, in mg) on patient

Chi-Square Analysis for Dietary Habits and Exercise Frequency

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

Coffee Shop Drink Preference

A survey at a coffee shop collected responses from 120 customers regarding two categorical variables

Comparing Effectiveness of Educational Workshops

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

Customer Return Rates for Two Brands

A market research firm collected data on customer return behavior for two competing clothing brands.

Customer Satisfaction: Online vs In-store Shopping

A retail company surveyed its customers about their satisfaction with online versus in-store shoppin

Elderly Health Program Evaluation

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

Exploring Temperature and Ice Cream Sales

A study was conducted to explore the relationship between daily temperature (in °F) and ice cream sa

Health Study on Diet and Activity

A health study investigated the relationship between diet type (Vegetarian vs. Non-vegetarian) and a

Housing Prices and Square Footage Analysis

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

Impact of Skewness on the Sampling Distribution of the Sample Mean in Bivariate Data

A researcher collects data on household income (x) and spending on luxury goods (y), noting that inc

Influential Points and Leverage in Salary vs. Experience

A human resources department collected data on 20 employees, recording their years of experience (X)

Interpreting Calculator Output for Regression Analysis in Sports

A sports researcher investigates the relationship between players' height (in cm, X) and their free

Political Preference by Demographic Group

A survey was conducted to explore the relationship between age group and political party preference.

Public Health Campaign on Smoking Cessation

A public health department launched a campaign to help individuals quit smoking. A study was conduct

Residual Analysis and Outlier Detection in a Weight Loss Study

A weight loss program is evaluated by predicting weight loss (in pounds) using a regression model ba

Restaurant Order Survey

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

Restaurant Tip Analysis

In a study of restaurant bills, data were collected on the total bill amount (in dollars) and the ti

Retail Promotions: Sales vs Advertising Budget

A retail chain recorded weekly data (n = 20) on advertising budget (x, in thousand dollars) and week

Scatterplot Analysis: Teen Social Media Usage

A study collected data on the number of close friends (X) a group of teens reported and the number o

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 Comparison of Unstandardized vs. Standardized Regression Coefficients

A data analyst performs a simulation study to compare the sampling distributions of unstandardized a

Simulation-Based Investigation of Chi-Square Distribution in Two-Way Tables

A researcher is interested in the chi-square test for independence in a two-way table. To understand

Smartphone Brand Loyalty

A market survey examined customer satisfaction across three smartphone brands (Brand X, Brand Y, and

Website Click-Through Rate

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

Analyzing Bias in Convenience Sampling at a Mall

A researcher conducts a convenience survey at a local shopping mall to gauge consumer satisfaction w

Analyzing Survey Bias in Voluntary Response Surveys

A local newspaper conducts a voluntary response survey asking residents about their satisfaction wit

Assessing Sampling Techniques in Market Research for a New Product

A company plans to gauge consumer preferences for a new product by sampling shoppers at a busy mall

Assessing the Impact of Sampling Bias through Simulation

A researcher suspects that a nonrandom sampling method may introduce bias into estimates of a popula

Central Limit Theorem and Coffee Consumption

In a certain region, the average daily coffee consumption is 3 cups with a standard deviation of 1 c

Cluster Sampling in Educational Research

A researcher wants to study academic performance across a large school district. The district is div

Comparative Simulation of the Mean and Median Sampling Distributions

A researcher simulates 1000 samples of size $$n = 30$$ from a moderately skewed population and calcu

Comparing Two Treatments in a Medical Study

A clinical trial compares two treatments for lowering blood pressure. Treatment A (n = 25) results i

Customer Satisfaction Proportion Sampling

A company has found that 80% of its customers are satisfied with its service. A survey is conducted

Customer Satisfaction with New vs. Old Product

A market research survey was conducted to compare customer satisfaction between a new product and an

Designing a Stratified Random Sample for Student Opinions on Distance Learning

A researcher intends to survey high school students' opinions on the transition to distance learning

Diet, Weight Loss, and Regression Analysis

A nutritionist is studying the relationship between daily caloric intake (Calories) and observed wei

E-Commerce Website Redesign and Consumer Behavior

An online retailer has redesigned its website and wants to assess whether the change has affected co

Effects of Diet Programs on Weight Loss

Researchers compared the effectiveness of two diet programs versus a Control group in achieving sign

Environmental Pollution and Respiratory Health

Public health officials are studying the relationship between exposure to particulate matter (PM2.5,

Experimental Design: Evaluating a Review Course for SAT Scores

A study aims to evaluate whether a new SAT review course improves student scores. Students are rando

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.

Impact of a Training Program on Employee Productivity

A company measured employee productivity before and after a new training program. Two independent sa

Impact of Diet on Weight Loss Success

A nutritionist compared the success rates of two different diet plans. Under Diet A, 45 out of 75 pa

Investigating Data Variability in Statewide Math Test Scores

A state education board uses multiple samples to estimate average math test scores across high schoo

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

Lottery Wins and Rare Event Probability

In a lottery, the probability of winning a small prize is 0.001 for each ticket. If 10,000 tickets a

Matched Pairs Experiment for Diet and Exercise in Blood Pressure Study

Researchers are studying the effects of two different diets combined with varying exercise regimens

Music Therapy and Stress Levels

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

Online vs. In-Person Shopping Preferences

A market research company surveyed shoppers to understand their preferred mode of shopping (Online v

Physical Activity Levels by Region

A health study surveyed residents in different regions to assess their physical activity levels (cat

Predicting Blood Pressure from Age: Regression and Inference

A health researcher is examining the relationship between the age of adults and their systolic blood

Remote Learning Effectiveness

At a high school, the impact of transitioning to remote learning on student test scores is studied u

Replication in an Agricultural Experiment

An agricultural scientist is testing the effectiveness of two fertilizers on crop yield. The experim

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 Sampling Distributions for Quality Control in Manufacturing

A manufacturing company produces items that are expected to weigh $$500 \text{ g}$$ on average with

Survey Design: Improving Question Wording

A market research company is designing a survey for a new product but finds that several questions m

Survey on Public Opinion Regarding Public Transit

A survey of 200 city residents was conducted to assess support for an increase in public transit fun

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

Volunteer Firefighter Response Times

A prospective study of volunteer firefighter response times records data from 45 incidents. The samp

Car Purchase Decisions by Region

A car dealership surveyed buyers about their vehicle type by region. The data are summarized below:

Casino Free Chips Expected Sum

A casino offers free chips to couples. One person draws a card from Bag X containing the numbers $$\

Charity Lottery Expected Outcome

A charity sells 10,000 lottery tickets at $1 each with one prize of $7500. Let $$X$$ represent the n

Charity Lottery Expected Value Analysis

A charity sells 10,000 lottery tickets at $$\$1$$ each. One ticket wins a prize of $$\$7500$$, while

Coffee Consumption and Alertness Level Regression Analysis

A study examines the influence of coffee consumption (number of cups per day) on an individual's ale

Cumulative Probability Distribution in AP Exam Scores

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

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

Evaluating a New Teaching Technique in High School

A school district is testing a new interactive teaching technique against the traditional method. Ce

Fitness Class Participation by Age Group

A gym surveyed 300 members about their preferred fitness class types. The results by age group are d

Highway Construction Productivity Analysis

The daily output of highway construction (in miles) depends on weather conditions as follows: | Wea

Investment Returns: Sum and Difference of Random Variables

An investor has two independent investments with the following annual return distributions: Investm

Manufacturing Quality Control for Defects

A factory produces electronic components, and historically the defect rate is expected to be less th

Multi-center Clinical Trial for a New Vaccine

A large-scale clinical trial is conducted across several hospitals to evaluate the efficacy of a new

Online Advertisement Click-Through

A digital marketing campaign delivers 200 ad impressions, where each impression has a 3% chance of g

Random Variable Transformation in a Carnival Game

A carnival game offers three possible payouts: $$\$2$$ with probability 0.5, $$\$5$$ with probabilit

Sampling Distribution of the Interquartile Range (IQR) via Simulation

A simulation is performed to calculate the interquartile range (IQR) for samples drawn from a non-no

Sampling Distribution of the Sample Mean from a Normal Population

A simulation experiment draws repeated random samples from a normally distributed population with $$

Simulated Distribution of the Difference of Sample Means

In a simulation comparing two independent groups (for example, treatment and control), separate samp

Simulating the Expected Value in a Lottery Game

Consider a lottery game with payouts given by the following probabilities: $$P(\$2)=0.5$$, $$P(\$5)=

Social Media Post Engagement

A social media analyst is studying the engagement on posts from a popular brand. A random sample of

Student Exam Score Distribution

An exam produces scores in the following intervals with corresponding percentages. Use the midpoints

Testing Customer Satisfaction Claims

A coffee shop claims that 80% of its customers are satisfied. To test this claim, a random sample of

Transforming Payouts in a Carnival Game

A carnival game pays out according to a random variable $$X$$ with outcomes: $10 (p = 0.4), $20 (p =

Assessing Estimators in Quality Testing

A factory uses different methods to estimate the maximum durable weight of a product. Five estimator

Bootstrapping and the Sampling Distribution of the Mean

A researcher collects daily sales data from a small store over 30 days. The observed sample mean is

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 Biased Estimators via Simulation Outcomes

A simulation study compares two estimators for a population parameter. Estimator A has a constant bi

Comparing Class Test Scores

Two independent classes took a standardized test. Class X (with $$n=30$$) had a mean score of 78 wit

Comparing Clinical Trial Drug Effects

In a clinical trial, two drugs are used to lower blood pressure. Drug A produces an average reductio

Comparing Durability of Lightbulbs

A study was conducted to compare the longevity of light bulbs manufactured by two different factorie

Constructing a 95% Confidence Interval for Battery Lifetime

A quality control study tests the lifetimes of batteries. A random sample of 50 batteries has a samp

Difference in Sample Means: Genetic Mutations and Parental Age

Research indicates that 40-year-old men contribute an average of $$65$$ genetic mutations to their c

Effect of Outliers on Sampling Distribution of the Mean

A dataset on household incomes is highly skewed due to extreme values. A statistician takes random s

Effect of Sample Size on Variability of Estimator

A researcher collects repeated samples from a population with a known mean of $$\mu = 100$$ and stan

Election Polling Proportions

In a pre-election survey, it is known that 52% of voters favor a certain candidate. A random sample

Employment Benefits Perception

A company surveyed its employees regarding their perception of employment benefits. The responses ar

Impact of Sample Size on Variability

A researcher is analyzing daily website visits. In an initial study with 30 days, the sample standar

Manufacturing Process Consistency and Variability

A manufacturer recently implemented a new process intended to reduce variability in product weights.

Political Opinion Poll on Policy Support

A political opinion poll was conducted to determine the relationship between political affiliation a

Sampling Distribution for Differences in Sample Means: Academic Test Scores

Two classes are compared on a standardized test. Class A has a population mean of 78 with a standard

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 $$\

Simulated Daily Sales Distribution

A retail store simulated its daily sales over several months. The resulting sampling distribution of

Simulated Sampling Distribution for Eco-Friendly Vehicle Mileage

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

Social Media Engagement Proportions

A social media platform reports that 65% of its users engage with sponsored content. A random sample

Training Techniques and Marathon Finish Times

A sports scientist is comparing the effectiveness of two training methods on marathon finish times.

Using TI-84 for Z-Score Calculations in Sampling Distributions

A study on academic performance finds that student test scores are normally distributed with a mean

Voting Behavior by Gender

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

Analyzing Election Poll Data: Estimating the Margin of Error

An election poll of 1000 voters produced a sample proportion of $$\hat{p}=0.48$$ for Candidate A. As

Analyzing Proportions as a Function of Batch Size

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

Assessing New Advertising Campaign Effectiveness

A company runs a new advertising campaign. Out of 400 customers, 160 made a purchase within 24 hours

Blood Donation Campaign Study

A local health department funds two different public campaigns to increase blood donation rates. One

Campaign's Voter Turnout Comparison

A political campaign is studying voter turnout in two neighboring cities. In City A, a survey of 400

Checking Inference Conditions for Proportion Data

A quality control study on a production process sampled 50 items and found that 47 met quality stand

Comparing Proportions in Education Methods

A study compares pass rates for students taught by two different methods. For Method A, 96 out of 12

Comparing Test Pass Rates

A study compares the pass rates of two types of schools. The following table summarizes the results:

Comprehensive Analysis of Confidence and Significance in Survey Data

A political researcher conducted a two-part survey to analyze voter opinions on a new policy. The fi

Customer Satisfaction in a Retail Store

A large retail chain conducted a survey to measure customer satisfaction. Out of a simple random sam

Digital Platform Success Rate Comparison

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

Environmental Study: Testing Proportion Exceeding Safety Threshold

A study of water quality in a river found that 18 out of 90 samples exceeded the safety threshold fo

Evaluating Public Support for a Tax

A poll was conducted to measure public support for a proposed tax. In the first survey, 1000 voters

Evaluating Trends in Graduation Rates

Over a span of 10 years, a school district has recorded the annual graduation rates. A scatterplot o

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

Health Intervention Program Effectiveness

A public health agency is evaluating a new intervention designed to increase the proportion of indiv

Health Study: Smoking Prevalence Comparison

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

Medical Trial: Comparing Treatment and Control

A clinical trial compares the effectiveness of a new treatment with a placebo. In the treatment grou

Political Polling: Estimating Voter Support

In a random sample of 800 voters, 464 indicated support for Candidate A. Answer the following questi

R&D Investment Success Rate

Two companies are comparing the success rates of their R&D investments. Company X had 100 projects w

STEM Club Gender Representation Study

A high school is investigating the proportion of female members participating in its STEM clubs. Par

Testing for a Rare Event Proportion

An environmental study collected 1000 water samples to test for a rare pollutant. Only 4 samples tes

Urban vs. Rural: Survey on Public Transportation Usage

A survey was conducted to compare the use of public transportation between urban and rural residents

Urban vs. Suburban Crime Reporting Rates

A survey was conducted to compare feelings of safety in urban and suburban areas. In an urban sample

Voter Preference Comparison: Confidence Interval and Hypothesis Test

In a study of voter preferences, two independent samples were taken. In District A, a sample of 200

Average Daily Sales at a Retail Store

A retail manager records the daily sales (in thousands of dollars) over a period of 20 days. The sam

Battery Life Study

A battery manufacturer claims that the new battery model has an average lifespan of $$\mu$$ hours. A

Blood Pressure and Sodium Intake Regression

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

Comparative Analysis of Blood Pressure Between Population Groups

Public health officials are comparing systolic blood pressure levels between an urban population and

Comparison of Waiting Times: Urban vs. Rural Hospitals

A health researcher compares patient waiting times in emergency rooms between urban and rural hospit

Customer Preference on Smartphone Features

A market research survey evaluates customer satisfaction for two smartphone brands, Brand A and Bran

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

Customer Wait Time in Service

A supermarket manager records the wait times (in minutes) for customers at a checkout counter. In a

Difference in Mean Cholesterol Drop between Diet Plans

A nutritional study compares two diet plans. For Diet A, a sample of 50 participants shows an averag

Effectiveness of a Diet Program: Paired Weight Loss Study

Twenty individuals participated in a 6-week diet program. Their weights were recorded before and aft

Effectiveness of a New Study Method on Test Scores

A tutoring program is implemented in a school, and the same group of 12 students is tested before an

Effectiveness of a New Teaching Method

A school district wants to evaluate the effectiveness of a new teaching method on student test score

Employee Training and Productivity Outcome

A company examines whether the type of training (Online vs. In-person) affects employee productivity

Engine Emissions Compliance

An environmental agency is monitoring engine emissions to ensure compliance with regulations that re

Impact of Advertising on Product Awareness

A marketing team wants to analyze the effect of advertising on product awareness. Consumers are cate

Machine Downtime Analysis

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

Manufacturing Process Improvement

A manufacturing company implements a new process intended to reduce component production times. For

Project Completion Times

A company is evaluating the effect of a process improvement by comparing project completion times be

Quality Control in Food Packaging

A snack food company advertises that its bags contain 305 grams of product. To ensure quality, a ran

Reaction Time One-Sample t-Test

A psychologist is testing whether a new stimulus affects human reaction times. In a study of 15 indi

Reaction Time Testing Under Caffeine Effects

A study examines the effect of caffeine on human reaction times. Two independent random samples of 2

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

Study Hours and Exam Scores Regression

A teacher collects data from 40 students relating the number of study hours (x) to exam scores (y).

Study Hours and Test Scores

A teacher implements a new study method to improve student performance. Eight students are tested be

Study of Daily Traffic Flow

A transportation engineer studies the flow of traffic on a busy freeway. Data collected over 50 rand

Test Score Improvement Analysis in a Preparation Class

In an SAT preparation class, 25 students took a pre-test and a post-test. The improvements (post-tes

Analyzing Website Navigation: Chi-Square Test for Independence

A study examining whether the navigation path taken on a website is related to the type of device us

Assessing the Fit of a Theoretical Distribution for Disease Rates

A health researcher claims that the incidence of a particular disease in a population is distributed

Blood Type Distribution: Goodness-of-Fit Test

A study of 400 individuals reports the following observed counts for blood types: O = 180, A = 120,

Candy Color Distribution Goodness-of-Fit Test

A candy manufacturer claims that the distribution of candy colors in a bag is 30% red, 20% blue, 25%

Clothing Preference and Gender: Test for Independence

A clothing store surveyed customers to see if there is an association between gender (male, female)

College Major vs Gender: Chi-Square Test for Independence

A college survey recorded the number of students by major (Science, Humanities, Business, Arts) and

Computer Usage and Major Association Independence Test

At a university, students are classified by their computer usage frequency (Low, Medium, High) and b

Diet Preference Among Athletes

In a study, three groups of athletes (Football, Basketball, Soccer) were surveyed regarding their di

Distribution of Housing Types in a City

A city planning department is examining the distribution of housing types in the city. They expect t

Effect of Marketing Campaign on Brand Awareness

A company wishes to determine if exposure to its marketing campaign is associated with brand awarene

Effectiveness of Advertisement Types

A study assesses whether the type of advertisement affects perceived effectiveness. Three ad types a

Evaluating Marketing Strategies: Chi-Square Test for Independence with a Simulation Component

A marketing firm wants to determine if there is an association between consumer purchase behavior (B

Exercise Frequency and Music Preference – Chi-Square Test for Independence

A gym surveyed 150 members to study the relationship between exercise frequency (categorized as Low,

Goodness-of-Fit for Beverage Preferences

A local cafe expects customer beverage preferences to follow the distribution: Iced Coffee (40%), Ho

Goodness-of-Fit Test for Dice Fairness

A six-sided die is suspected of being biased. In an experiment of 120 rolls, the observed frequencie

Homogeneity in Customer Service Satisfaction Across Branches

A retail chain wants to determine if customer satisfaction (Satisfied, Neutral, Unsatisfied) is homo

Independence of Smoking and Lung Disease

A public health survey collected data from 300 participants to investigate the relationship between

Music Genre Preferences Across Cities – Chi-Square Test for Homogeneity

A market research firm surveyed residents in four different cities (City A, City B, City C, City D)

Pet Ownership and Residence Type Independence Test

A city survey collected data on pet ownership (Owning a pet, Not owning a pet) and type of residence

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

Quality Control in a Factory

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

Social Media Platform Usage and Age: Test for Independence

A survey of 400 individuals collects data on their most-used social media platform (Platform A, Plat

Sports Preferences by Gender: Chi-Square Test for Independence

A survey of 300 students recorded their preferred sport (Basketball, Soccer, Tennis) and their gende

Student Extracurricular Activities: Chi-Square Goodness-of-Fit

A high school believes that student interest in extracurricular activities (Sports, Music, Drama, Cl

Test for Independence: Political Opinions on Climate Change

A survey of 400 registered voters categorized by party affiliation (Democrats, Republicans, Independ

Travel Mode and Environmental Concern – Chi-Square Test for Independence

A survey of 250 commuters collected data on their primary travel mode (Car, Public Transit, Bike) an

Voter Preferences Among Four Candidates – Chi-Square Goodness-of-Fit

An election poll of 800 voters reports the following counts for four candidates: Candidate A: 220, C

Advertising and Sales Revenue Regression Analysis

A marketing firm is studying the relationship between advertising spending (in thousands of dollars)

Advertising Budget and Store Revenue: Chain Comparison

A retail company analyzed the effect of advertising spending (in thousands of dollars) on monthly st

Agricultural Study: Fertilizer and Crop Yield

In an agricultural study involving 52 plots, researchers investigated the effect of fertilizer usage

Blood Pressure and Sodium Intake Study

A study investigating the relationship between daily sodium intake (measured in mg) and blood pressu

Car Fuel Efficiency and Car Weight Regression Analysis

An automotive engineer analyzes the relationship between a car's weight (in kg) and its fuel efficie

Consumer Spending and Income Levels

An economist analyzed data from 60 households to study the relationship between household income (x,

Crop Yields and Fertilizer Usage

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

Customer Wait Time and Satisfaction Ratings

A call center is analyzing whether average wait time ($$x$$, in minutes) affects customer satisfacti

Effectiveness of a New Drug on Blood Pressure

A pharmaceutical company is investigating whether a new drug reduces blood pressure as the dosage (i

Energy Consumption Analysis

A utility company is investigating the relationship between outside temperature (in °F) and resident

Evaluating the Impact of Work Experience on Promotion Rate

An organizational study examines whether years of work experience (x) affect the promotion rate (y,

Exercise Time and Calorie Burn

A fitness app tracks the number of minutes spent exercising (x) and the number of calories burned (y

Fitness Tracker Study: Daily Steps and Weight Change

A fitness study examined whether daily steps (x, in thousands) predict weekly weight change (y, in p

Industrial Emissions and Air Quality

A governmental agency is evaluating the impact of industrial emissions (x, in tons per day) on local

Machine Runtime and Maintenance Costs

An operations manager is investigating whether the total runtime of an industrial machine (in hours

Medication Dosage and Blood Pressure Reduction

A hospital study evaluated the effect of increasing medication dosage on blood pressure reduction. T

Online Advertisement View Time and Purchase Likelihood

A study examines the relationship between the time spent viewing an online advertisement ($$x$$, in

Online Engagement and Sales Conversion

An e-commerce analyst studied the relationship between average time spent on a website (in minutes)

Sleep Duration and Reaction Time

A researcher studies the relationship between nightly sleep duration (in hours) and reaction time (i

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 Influence on Product Sales Simulation

A business analyst wants to understand the effect of time spent on social media advertising (in hour

Social Media Use and Academic Performance

A study examines whether daily social media usage (x, in hours) is related to students' GPAs (y, on

Temperature Impact on Soft Drink Sales

A beverage company studies the relationship between daily high temperatures (x) and soft drink sales

Weather Forecasting: Humidity vs. Chance of Precipitation

Meteorologists studied the relationship between relative humidity (x, in percentage points) and chan

Weather Prediction Model: Slope Simulation

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

Weekly Hours Worked and Job Productivity

A manufacturing plant studied the relationship between weekly hours worked (x) and job productivity