AP Statistics FRQ Room

Analysis of Categorical Data from Elections

A recent survey sampled 1000 voters to determine their preferred candidate in a local election. The

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

Application of the Empirical Rule to IQ Scores

Assume that IQ scores are normally distributed with a mean of $$100$$ and a standard deviation of $$

Boxplot Comparison: Stock Price Fluctuations Over Years

A company's daily stock prices over five consecutive years are summarized in the following table: |

Car Fuel Efficiency Test

A study measures the fuel efficiency of a sample of 50 cars. The sample has a mean miles per gallon

Comparing Pass Rates for Two Classes

In a high school, two math classes took the same standardized test. In Class 1, 28 out of 35 student

Constructing a Frequency Histogram from Commute Times

A study recorded the commute times (in minutes) for 20 individuals. The raw data are: $$\{12, 15, 1

Effect of Constant Adjustments on Mean Salary

Consider the salaries (in dollars) of six employees given below: $3,000; $7,000; $15,000; $22,000; $

Effects of Linear Transformation on Data

Let a data set $$X$$ have a mean of $$\mu$$ and a standard deviation of $$\sigma$$. Suppose we defin

Employee Benefits Satisfaction Interval

A company conducted a survey on employee satisfaction with benefits. Out of a sample of 120 employee

Employee Salary Adjustments

A company has six employees with the following salaries (in dollars): $$\{3000, 7000, 15000, 22000,

Error Rates in Two Production Machines

A factory operates two machines that produce the same part. Machine A produced 300 parts with 12 def

Evaluating a Histogram for Skewness in Temperature Data

A histogram shows the distribution of daily temperatures (in °F) during a summer month. The histogra

Examining Data Variability in Sports Statistics

A boxplot summarizes the points per game for a basketball player over a season with the following va

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

Impact of Incentives on Survey Participation

A market survey was carried out with two groups: one received an incentive and the other did not. In

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)

Marketing Campaign Reach by Region

A company tracked responses to a marketing campaign in two regions (Region 1 and Region 2) categoriz

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

Online Course Satisfaction Hypothesis Test

A university is evaluating the satisfaction level with its online course. In a survey of 200 randoml

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

Political Polling: Candidate Preference

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

Quality Control in Manufacturing

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

Rainfall Occurrence: Binomial Model

In a 31-day month (e.g., July), the probability of rain on any given day is $$0.2$$.

School Survey on Categorical Preferences

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

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 Usage and Employee Productivity

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

Study Program Effectiveness Hypothesis Test

A researcher wants to determine if a new study program increases test scores. In a random sample of

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

Analysis of Marketing Campaign Data: Sales vs. Advertisements

A company conducted a marketing campaign across several regions and recorded the amount spent on adv

App Usage Trend: Free vs Premium Users

A tech company is studying how frequently users utilize a particular feature in their app. Two group

Bootstrap Simulation for the Regression Intercept's Sampling Distribution

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

Comparing Marginal and Conditional Distributions in a Two-Way Table

A car dealership survey recorded data on car color and type. The dealership is interested in the dis

Complex Survey Analysis: Income and Expenditure Patterns

A national survey collects data on household income (in US dollars) and monthly expenditure (in US d

Consumer Product Satisfaction

A market research study evaluates consumer satisfaction with two new smartphone models. After using

Customer Loyalty Program Analysis

A retail company collected data on the number of store visits (x) by loyalty card members and the po

E-Commerce Site Traffic and Revenue Analysis

An e-commerce website collected data on daily visitor counts (x) and corresponding sales revenue in

Email Marketing Response Rates

A company ran two email marketing campaigns and recorded the number of recipients who responded and

Environmental Study: Air Pollution vs. Respiratory Issues

A public health researcher collects data from 50 cities to examine the relationship between air poll

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

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

Least Squares Regression for Predicting House Prices

A real estate analyst collected data on several houses detailing their square footage (X) and corres

Monte Carlo Simulation: Effect of Nonlinearity on Pearson's Correlation

A statistician uses Monte Carlo simulation to explore how nonlinearity in data affects the sampling

Movie Genre Preference and Age Group

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

Reverse Regression: Predicting Hours Worked from Earnings

Consider a regression model for predicting earnings (Y, in thousands of dollars) from hours worked p

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 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-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

Social Media Use and Academic Performance

A study was conducted on 50 high school students to investigate the relationship between daily hours

Temperature and Ice Cream Sales

A study over 30 days recorded the average daily temperature (in °F) and corresponding ice cream sale

Workforce Diversity Study

A corporation conducted a study to analyze the distribution of employees across different job levels

Adverse Reaction Probability in a Drug Trial

In a clinical trial for a new drug, each patient has a 5% chance of an adverse reaction. In a sample

Analyzing Sampling Variability Using Boxplots

A study on the ages of high school teachers uses four different sampling methods (A, B, C, and D) to

Bias in Random Digit Sampling

A researcher uses random digit dialing to contact households for a survey. However, certain demograp

Central Limit Theorem Demonstration Through Simulation with an Exponential Population

A researcher is interested in the Central Limit Theorem (CLT) and performs a simulation by drawing s

Comparing Customer Satisfaction Across Two Store Locations

A retail company conducted a survey to measure customer satisfaction at two store locations, Store X

Customer Feedback for a New Product

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

Double-Blind Experiment Design for Nausea Reduction

A research team is testing a new wristband designed to reduce postoperative nausea. To eliminate pla

Effect of Noise Levels on Sleep Quality

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

Evaluating a New Teaching Method

A study compares a traditional teaching method and a new teaching method. In an independent study, 3

Flu Vaccination Campaign and Illness Spread

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

Hypergeometric Distribution in Quality Inspection

In a batch of 200 items, 10 are known to be defective. A quality inspector randomly selects 20 items

Impact of Sample Size on Variability

In a study investigating average daily water consumption, two different sample sizes are used: one s

Internet Usage and Education Level

A study analyzed internet usage frequency (Daily, Weekly, Rarely) among individuals with different e

Investigating Voluntary Response Survey Bias

A mid-sized university is conducting an online survey about campus safety. The survey is distributed

Online Tutoring and Student Performance

A school district implements an online tutoring program aimed at improving student math performance.

Randomized Controlled Trial: Vaccine Efficacy

A clinical trial is conducted to evaluate a vaccine. 200 subjects receive the vaccine and 200 receiv

Remote Learning and Student Engagement

A school district wants to evaluate the effectiveness of remote learning on student engagement. Data

Remote Learning Effectiveness

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

Sampling Variability in Teacher Performance Evaluations

A school district collects teacher performance evaluations through student surveys. The administrati

Simulation of the Sampling Distribution of the Sample Variance

A researcher runs a simulation to approximate the sampling distribution of the sample variance from

Smartphone Usage and Sleep Quality

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

Weather Patterns and Traffic Accidents

City officials are investigating the relationship between adverse weather conditions and the frequen

Ad Spend and Market Share Regression Analysis

A market analyst investigates the relationship between advertising spend (in millions of dollars) an

AP Exam Score Distribution: Cumulative Probability Analysis

The table below shows the percentage of students achieving each AP exam score for a given year.

Binomial Process in Quality Testing

A quality control inspector tests a batch of 100 light bulbs. Each bulb has a 10% chance of being de

City Traffic Speed Analysis

The city transportation department collected data on the speeds of vehicles on a major highway. A ra

Comparing Sampling Distributions Under Different Population Variabilities

A simulation is run for two populations: Population A has a low variance and Population B has a high

Defect Rate Comparison between Two Factories

A manufacturing company is studying defect rates in two of its factories. Factory 1 produced 1000 it

Defective Light Bulb Binomial Probabilities

Suppose the probability that a light bulb is defective is $$0.1$$. Consider independent selections o

Drug Effectiveness Study

Researchers conducted a clinical trial comparing a new drug to a placebo. The recovery outcomes are

Effect of Fertilizer Type on Plant Growth

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

Effectiveness of Public Health Announcements on Mask-Wearing Behavior

During a flu outbreak, a health department launches a public health campaign to encourage mask-weari

Employee Turnover Comparison in Two Departments

A company collected data on employee retention in two departments. In Department X, 45 out of 60 emp

Event Planning and Rainy Days: Binomial Analysis

An event planner considers a month of 30 days where the probability of a rainy day is $$0.3$$, indep

Geometric Distribution: Encountering an Honest Man

In a certain ancient society, the probability that a randomly selected man is honest is $$0.12$$. As

Highway Construction Productivity Analysis

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

Highway Construction: Expected Daily Miles

A highway construction project operates under varying weather conditions. On a clear day, workers la

Investigative Study on Public Health Intervention

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

Lottery Expected Value

A charity lottery sells 5000 tickets at $$\$2$$ each. One winning ticket receives a prize of $$\$500

Manufacturing Process Downtime

A factory records daily machine downtime (in hours) due to equipment failures according to the follo

Online Shopping Behavior by Time of Visit

An e-commerce website collected data on visitor behavior during different times of the day. The tabl

Quality Control in Manufacturing

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

Quality Control in Manufacturing

A factory produces items with a defect probability of $$0.05$$ per item. Items are produced in batch

Restaurant Order Times

A fast-food restaurant records its order preparation times (in minutes) with the following distribut

Sales Calls Geometric Distribution

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

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)=

Smartphone Usage and Sleep Quality Regression Analysis

A study investigates whether the number of hours spent on a smartphone before bedtime affects sleep

Stock Market Daily Returns

A particular stock’s daily percentage return is modeled by a discrete random variable with the follo

Student Test Scores and Conditional Probabilities

A school's data on test strategies and score ranges is summarized in the tables below. Table 1: Str

Website Session Duration Analysis

A tech company is analyzing website usage and wants to estimate the typical duration of user session

Bacterial Count in Water Samples

A water quality test measures the concentration of bacteria (in CFU per 100 ml) in a river. The popu

Battery Life Analysis Using Normal Distribution

A battery manufacturer claims that the lifespan of its batteries is normally distributed with mean $

Comparing Juice Bottling Process

A juice company compares its bottling process with that of a competitor. A random sample of 50 bottl

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 $$1$$

Critical Values for Beverage Fill Weights

A beverage company claims that its bottles contain 1 liter of liquid on average with a standard devi

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 Sample Size on Standard Error

Consider a population with a standard deviation of $$\sigma = 12$$. Samples are drawn to estimate th

Employee Productivity by Shift

A company is examining the relationship between work shift (Morning vs. Evening) and productivity le

Employment Benefits Perception

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

Estimator Bias: Maximum vs. Mean in Soccer Scores

A soccer coach considers using the maximum number of goals scored in a series of 10 games as an esti

Estimator Evaluation in Baseball Manufacturing

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

Evaluating Manufacturing Estimators

A factory produces widgets with a true length of 150 mm. Five different estimators (A, B, C, D, and

Evaluating Sample Proportions in a Survey

A campus dining satisfaction survey indicates that 70% of all students are satisfied with the dining

Examining Bias in Sample Maximums

In a quality control study, an analyst records the maximum defect size from samples of 10 items take

Impact of Sample Size on Variability

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

Math Anxiety Brain Activity Proportions

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

Normal Approximation to the Binomial in Sampling Distributions

A factory has a light bulb defect rate of 2%. In a shipment of 500 bulbs, let X represent the number

Public Health Study: Vaccination and Illness

In an effort to study the relationship between vaccination status and illness, public health officia

Quality Control of Widget Weights

A factory produces widgets with weights that are normally distributed with $$\mu = 100$$ grams and $

Sampling Distribution of the Maximum: Weather Temperature Extremes

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

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

Social Media Engagement Proportions

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

Student Performance and Study Techniques

A study compared two study methods: using flashcards versus summarization. In the flashcards group (

Technology Use and Academic Major

A survey was conducted to examine the relationship between academic major and technology usage frequ

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

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

Assessing New Advertising Campaign Effectiveness

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

Assessing Website Conversion Rate

A company claims that its website has a conversion rate of 5%. To test this claim, a random sample o

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 Participation Rates in Exercise Programs Across Cities

Two cities conducted surveys about participation in exercise programs. City X had 250 participants o

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 Two Methods for Quality Control in Manufacturing

A manufacturing company compares two quality control methods. In a trial run, Method A identified 95

Comparing Two Teaching Methods: Confidence Interval for Difference in Proportions

A study compared the effectiveness of two teaching methods. In a sample of 150 students taught by Me

Computer Literacy Workshop Study

A community center is hosting two separate workshops aimed at improving computer literacy. At the en

Confidence Interval for a Population Proportion

A public opinion poll designed to estimate the proportion of voters who support a new policy produce

Customer Satisfaction Survey by Region

A retail company conducted a customer satisfaction survey in two regions, North and South. Responses

Determining Required Sample Size for Test Power

A public health researcher is testing the claim that the proportion of adults who smoke is less than

Drug Effectiveness: Hypothesis Testing for Proportion

A clinical trial involving 200 patients found that 154 recovered after treatment with a new drug. Th

Employee Retention in a Tech Firm

A tech company wants to analyze its employee retention rate. Out of a random sample of 200 employees

Estimating Customer Satisfaction

A local coffee shop surveyed 200 customers to assess their satisfaction. Out of the 200 customers, 1

Evaluating Trends in Graduation Rates

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

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

Healthy Meals Experiment Design

A college dining services wants to assess if a new healthy eating campaign increases the proportion

Marketing Campaign Response Rate Test

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

Online Advertising Impact Study

An online retailer wishes to study whether exposure to a particular digital advertisement increases

Planning a Comparative Survey

A researcher intends to conduct a survey comparing two groups and wants to detect a minimum differen

Product Defect Rates in Manufacturing

A manufacturing plant operates two production lines. Line A produced 1000 items with a defect rate o

Public Health: Smoking Rates by Region

A public health researcher wants to compare smoking rates between two regions. In Region 1, a survey

Reading Program Impact Study

A school district is testing a new reading program designed to improve students' reading proficiency

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. Suburban Crime Reporting Rates

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

Vaccine Hesitancy Survey Design

Public health officials are conducting a survey to estimate the proportion of individuals who are he

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

Voter Preferences by Age Group

A recent survey collected data on voter preferences for two political candidates among voters in two

Advertising Budget and Sales Performance Analysis

The scatterplot below represents data on a company's monthly advertising budget (in thousands of dol

Average Monthly Rainfall

Meteorologists are interested in the average monthly rainfall in a particular region. A random sampl

Caffeine Consumption and Reaction Times

A study aims to determine whether the consumption of caffeine affects reaction times. Two independen

Change in Manufacturing Process: Product Lifespan

A manufacturing company claims that a new manufacturing process increases the lifespan of its produc

Clinical Drug Trial: Comprehensive Data Analysis

A clinical trial is conducted to compare the effect of a new drug versus a placebo in lowering chole

Clinical Trial on Blood Pressure Reduction

A clinical trial is conducted to compare the effectiveness of two medications in reducing blood pres

Coffee Shop Wait Times

An urban coffee shop is interested in assessing its average customer wait time (in minutes) from pla

Comparing Two Methods of Estimating Reaction Time

A researcher is comparing two methods for measuring reaction time. Using Method 1 on a sample of 15

Comparison of Waiting Times: Urban vs. Rural Hospitals

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

Customer Satisfaction Survey

A company wants to evaluate customer satisfaction with two service channels: Online Chat and Telepho

Daily Energy Consumption Analysis: Hypothesis Test

A consumer agency is investigating a claim that a new brand of air-conditioning units uses only $$6.

Difference in Accident Rates

In a study of safety in a manufacturing plant, monthly accident data were collected for two independ

Effectiveness of a New Teaching Method

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

Effectiveness of Drug Treatments

A clinical trial compares two drug treatments (Drug X and Drug Y) for a certain condition. Patients

Effectiveness of Tutoring Program Investigation

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

Election Polling Power Analysis

In an election poll, a candidate claims to have 70% support. A critic believes the true support is 6

Engine Emissions Compliance

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

Examining Teaching Methods

A school is comparing two teaching methods: Traditional and Modern. Student outcomes are classified

Impact of a Diet Program on Weight Loss

A weight loss study measures the weight of 20 participants before and after a 6‐week diet program. T

Impact of Advertising on Product Awareness

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

Online Shopping and Customer Satisfaction

A retail company conducted a survey to assess customer satisfaction with its online shopping experie

Paired SAT Score Improvement

An SAT prep course reports that its students improved their scores. In a sample of 30 students, the

Paired t-Test for Sleep Duration with Meditation Program

A study is conducted to evaluate the effect of a four-week meditation program on sleep duration. For

Plant Growth under Different Fertilizers

A botanist is studying the effect of a new fertilizer on plant growth. A random sample of 12 plants

Power Analysis in a Drug Efficacy Study

A pharmaceutical company is testing a new drug intended to lower blood pressure. The test is a one-s

Production Efficiency Comparison Across Shifts

A factory compares production times between two work shifts. Shift A has a sample mean production ti

Quality Control Analysis using Simulation-Based P-Value

In a manufacturing process, quality control involves monitoring the variability of a key dimension u

Rainfall Measurement Study

A meteorologist records daily rainfall (in mm) over 20 days in a region. The sample has a mean of 12

Simulating the Sampling Distribution of Mean Light Bulb Lifetimes

A manufacturer runs a simulation to generate the sampling distribution of the sample mean lifetime f

Simulation of Sampling Distribution for Mean Crop Yield

An agricultural researcher is interested in the average crop yield (bushels per acre) of a particula

Simulation of Sampling Distribution for Mean Recovery Time

A hospital administrator runs a simulation study to assess the average recovery time (in days) after

Sleep Duration and Reaction Time Analysis

The scatterplot below shows data on hours of sleep (x-axis) and reaction time in seconds (y-axis) fr

Study Hours and GPA Analysis

The scatterplot below shows data on college students' weekly study hours (x-axis) and their GPA (on

Technology Adoption in Businesses

A market analysis explores the relationship between company size and the adoption of new technology.

Test Score Comparison between Two Classes

Two different classes took a standardized test. Class A (n = 30) had a mean score of 78 with a stand

Testing Mean Daily Coffee Consumption Claim

A claim is made that college students drink an average of at least 2.5 cups of coffee per day. A sur

Testing Mean Daily Water Consumption

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

Training Hours and Employee Productivity Analysis

The scatterplot below shows data on training hours (x-axis) and employee productivity, measured in u

Weekly Hours Worked and Earnings Analysis

The scatterplot below displays data relating weekly hours worked (x-axis) to weekly earnings in doll

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

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%

Clinical Trial: Treatment Effects on Recovery Rates

In a clinical trial, patients are randomly assigned to one of three treatment strategies (Treatment

College Major and Part-Time Job: Independence Test

A study examines the association between college major and part-time job status. The data collected

Customer Feedback Comparison: Chi-Square Test in Service Industry

A service company collected customer feedback regarding satisfaction levels (Satisfied, Neutral, Uns

Customer Satisfaction Survey Across Store Locations

A retail company conducts a survey to assess customer satisfaction across three store locations: Nor

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 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 7: Comparing Satisfaction Levels Across Service Centers

A company wants to determine if customer satisfaction is consistent across three service center bran

FRQ 8: Sports Participation and Academic Performance

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

FRQ 13: Customer Loyalty Across Store Branches

A chain store wants to investigate whether customer loyalty is consistent across its four branches.

Homogeneity in Customer Service Satisfaction Across Branches

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

Homogeneity in Patient Recovery Rates Across Hospitals

Three hospitals recorded recovery outcomes for a specific surgery. The outcomes are categorized as S

Homogeneity in Voter Turnout Among Demographic Groups

Exit polls in three different cities recorded voter turnout (Voted, Did Not Vote). Use the data to t

Preferred Payment Methods: Chi-Square Test for Homogeneity

A market research firm conducted surveys in three different cities regarding preferred payment metho

Quality Control in a Factory

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

Race Participation in Marathon

A marathon organizer expects the racial participation to follow these percentages: Group 1 = 30%, Gr

Satisfaction Survey Among Product Users: Chi-Square Test for Independence

A company wants to investigate whether customer satisfaction is independent of product type. A surve

Sports Participation and Gender – Chi-Square Test for Independence

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

Survey on Preferred Modes of Transportation

A city survey investigates residents’ preferred modes of transportation. The city’s transportation m

Traffic Light Malfunction Analysis

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

Type of Transportation and Commute Satisfaction

A survey of 530 commuters collected data on their primary mode of transportation (Car, Bus, Bike, Wa

Voter Preferences Across Regions: Homogeneity Test

A political analyst surveys 100 voters from each of three regions (North, South, Midwest) regarding

Voter Registration Distribution

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

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

Air Quality and Traffic Flow

A study investigates whether daily traffic flow (vehicles per hour) is associated with urban air pol

Assessing Environmental Pollution Impact

A study was conducted to assess the impact of vehicle count on NO2 levels in a city. A regression an

Coffee Consumption and Alertness

A study examines the relationship between cups of coffee consumed per day (x) and a measured alertne

Consumer Spending and Income Levels

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

Effect of Study Time on Test Scores

A teacher collects data on the number of hours studied (x) and exam scores (y) out of 100 for 25 stu

Engine Size and Emissions

An environmental engineer is studying the relationship between engine size (in liters) and vehicle e

Exercise Duration and Weight Loss

A fitness study explores the relationship between exercise duration (in minutes) and weight loss (in

Food Intake and Weight Gain in Mice

In an experiment with mice, researchers study the relationship between daily calorie intake ($$x$$)

House Size vs House Price

A real estate analyst is studying the relationship between house size (in square feet) and house pri

Impact of Outliers on Slope Simulation

A statistician is studying the relationship between weekly physical activity (in minutes) and weight

Impact of Study Hours on Exam Scores

A study examines the effect of weekly study hours ($$x$$) on exam scores ($$y$$) among 30 students.

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

Machine Calibration and Defect Rate

A manufacturing engineer is studying the impact of a machine's calibration setting ($$x$$) on its de

Medical Dosage and Blood Pressure Reduction

A clinical study examines the effect of a new drug dosage (x, in mg) on the reduction of blood press

Medication Dosage and Blood Pressure Reduction

A study investigates the effect of medication dosage (x, in mg) on blood pressure reduction (y, in m

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

Social Media Advertising and Customer Clicks

A digital marketer investigates the relationship between social media advertising spending (x, in th

Sports Training and Sprint Time

A coach investigates the relationship between the number of training hours (x) and sprint time (y, i

Student Performance and Study Hours

Researchers examine the relationship between hours studied (x) and exam scores (y). The regression a

Study Hours and SAT Scores: Private vs Public

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

Study Time and Exam Scores

A study was conducted to examine the relationship between hours of study (x) and exam scores (y) for

Temperature Effect on Ice Cream Sales

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

Vehicle Weight and Fuel Efficiency

A study investigates the relationship between vehicle weight (in pounds) and fuel efficiency (in mil

Weather Prediction Model: Slope Simulation

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