AP Statistics FRQ Room

Advertisement Design Impact on Customer Recall

A marketing company wants to test whether two different advertisement designs lead to differences in

Analysis of Weather Data: Daily Rainfall

A meteorologist recorded daily rainfall (in mm) over a month and summarized the data in the followin

Boxplot Comparison: Stock Price Fluctuations Over Years

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

Boxplot Construction from Exam Scores

Consider the following set of exam scores: $$\{15, 18, 22, 24, 24, 25, 27, 29, 30, 32, 35\}$$ Answ

Cafeteria Food Satisfaction Proportion

A college cafeteria conducted a survey to estimate the proportion of students who are satisfied with

Comparing Measures of Variability: IQR vs Standard Deviation

Consider the data set: {12, 15, 18, 21, 24, 27, 30}. Answer the following:

Comparing Sampling Distributions from Populations with Different Variances

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

Delivery Time Hypothesis Test

A fast-food chain advertises that its average delivery time is $$36$$ minutes. A consumer group coll

Digital vs. Traditional Lesson Impact on Class Attendance

A school district is testing whether interactive digital lessons lead to higher class attendance tha

Distribution of Heights in a Grade

A study on the heights (in centimeters) of students in a particular grade produced the following fre

Effect of Fertilizer Types on Tomato Yield

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

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

Evaluating a Histogram for Skewness in Temperature Data

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

Home Run Distances in Ballparks

The following set of home run distances (in feet) to center field in 13 ballparks is given: {387, 40

Home Run Distances: Mean, Median, and Outlier Impact

A dataset of home run distances (in feet) recorded in 13 ballparks is given as follows: {387, 400, 4

Interquartile Range and Boxplot Construction

Given the dataset: {12, 15, 16, 18, 20, 22, 25, 27, 30, 35}, perform an analysis of its distribution

Investigative Task: Evaluating a School Breakfast Program

A school district is considering a breakfast program aimed at improving student performance. Prelimi

Job Satisfaction Across Departments

A company administered job satisfaction surveys in two different departments. In Department 1, 120 o

Lottery Ticket Analysis

The probability of winning on a single lottery ticket is $$0.001$$. A person buys tickets one after

Nature Exposure and Mood Improvement

An environmental psychology study is designed to assess whether guided nature walks improve mood amo

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

Public Transportation Usage by Occupation

A survey of 240 workers recorded their public transportation usage (Regular, Occasional, Never) alon

Relative Frequency Calculation from Pet Ownership Survey

A survey regarding pet ownership in households produced the following frequency table: | Pets Owned

Sampling Distribution of the Sample Range for SAT Scores

A statistician is studying SAT scores whose distribution is known to have a certain degree of variab

Shipping Delays at a Warehouse

At a large distribution center, shipping delays (in hours) are approximately normally distributed wi

Simulated Sampling Distribution of the Standard Deviation

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

Simulation of Sampling Distribution of a Proportion in a Medical Recovery Study

In a clinical trial, suppose the true proportion of patients who recover from a treatment is 0.80. A

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

Call Center Quick Resolutions

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

Car Crash Safety Feature Evaluation

An automotive safety engineer evaluates two car models based on their performance in crash tests. Th

Coffee Shop Customer Survey Analysis

A coffee shop conducted a survey to determine customer preferences based on the type of beverage and

Comparing Regression Lines With and Without an Influential Point

A company collected data on its monthly sales (Y, in millions of dollars) and advertising spending (

Computing Regression Statistics from Summary Data: Advertising and Sales

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

Correlation vs. Causation Discussion

A study finds a high positive correlation between ice cream consumption and the number of drowning i

Cuteness Factor Study Revisited

A Japanese study collected data on 250 volunteers who were shown pictures of cute baby animals, adul

Effectiveness of a New Curriculum

A school district implemented a new curriculum in some of its schools and maintained the traditional

Housing Prices and Home Size

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

Impact of a New Study App on Academic Performance

A technology company has developed a new study application intended to improve academic performance.

Internet Usage and Credit Card Fraud

A cybersecurity study examined the relationship between frequency of internet usage and whether indi

Neighborhood Safety Survey

A community survey collected data on residents' sense of safety based on their neighborhood type (Ur

Online Course Enrollment Prediction

A university is analyzing the effect of the number of online advertisements (x) on online course enr

Recycling Attitudes Contingency Table Analysis

A survey of 200 community members was conducted to examine the relationship between recycling behavi

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

Social Media Use and Academic Performance

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

Social Media Use and Online Privacy

In a study on digital behavior, participants were surveyed about their level of social media usage (

Specialty Coffee Orders at a Coffee Shop

At a coffee shop, 25% of customers order a specialty coffee. In a random sample of $$60$$ customers,

Brand Satisfaction Survey Analysis

A company conducted a survey to evaluate the satisfaction level of its customers by gender. The resu

Comparing Beverage Effects on Pulse Rates

Researchers conduct an experiment to compare the effects of coffee, caffeinated cola, and herbal tea

Customer Satisfaction and Purchase Frequency: An Inference Study

A retail company surveys its customers regarding their satisfaction rating (on a 1–5 scale) and the

Data Collection in a Prospective Observational Study

A hospital conducts a prospective study to evaluate recovery times following a specific surgical pro

Designing a Stratified Sampling Plan for College Demographics

A university wants to estimate the average GPA for all its students. Given that the student populati

Effect of Noise Levels on Sleep Quality

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

Employee Job Satisfaction Survey

A company surveyed employees across three departments (Sales, HR, IT) regarding their job satisfacti

Evaluating a New Teaching Method

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

Evaluation of a New Teaching Method

An educational study compared a New teaching method with a Traditional one in terms of student exam

Factorial Experiment on Study Hours and Tutoring

A study is conducted to examine the effects of study hours and tutoring on student test scores. Stud

Flu Vaccination Campaign and Illness Spread

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

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 Response Time in Emergency Calls

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

Matched Pairs Design in a Dietary Study

A nutritionist wants to compare the effectiveness of two diets on weight loss. To control for initia

Matched Pairs Design in Educational Research

A school district is evaluating two teaching methods by having the same students experience both met

Modeling Nonresponse in Simulation of Sampling Distributions

A survey is conducted to measure the average household electricity usage. In the simulation, a rando

Observational Study Versus Experiment in Healthcare

A hospital wants to study the impact of a new dietary program on diabetic patients’ blood glucose le

Quality Control in Manufacturing

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

Randomized Controlled Trial: Vaccine Efficacy

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

Replication in an Agricultural Experiment

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

Sampling Methods in a Stratified Design

A researcher is studying the study habits of college students. The student population is divided int

Simulating the Effect of Sample Size on Standard Errors

A study is performed using simulation to assess how sample size affects the standard error of the sa

Simulation of the Sampling Distribution of the Sample Variance

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

Stratified Sampling in a City Demographics Study

A researcher intends to estimate the average household income within a large city by dividing the po

Understanding Sampling Error through Repeated Sampling

A researcher repeatedly draws independent simple random samples of size 50 from a large population w

Using Random Digit Tables in Clinical Studies

In designing a clinical study, researchers decide to use a random digit table to select a simple ran

Weather Patterns and Traffic Accidents

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

Bootstrap Sampling Distribution of the Sample Mean

A small dataset is provided, and a bootstrap resampling technique is applied to generate the samplin

Comparing Bank Loan Approval Rates

A bank uses two different underwriting policies. Under Policy A, 300 out of 500 applicants are appro

Comparing Consumer Spending at Two Malls

Two shopping malls record the average spending per visitor. Mall A has a sample of 100 visitors with

Comparing Simulation Results for Rainy Days

A simulation study recorded weather in two cities over a 30-day month. The results are as follows:

Comparison of Accident Rates on Highway Sections

A study on highway safety compared accident rates on two sections of a highway. On Section A, 5 acci

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

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

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:

Geometric Distribution in Reliability Testing

A machine in a factory has a 5% chance of failing on any given day. Let $$X$$ denote the day on whic

Geometric Distribution: Encountering an Honest Person

Imagine that the probability a randomly encountered man in ancient Greece is honest is $$0.12$$. Let

Impact of Meditation on Stress Reduction

A mental health clinic is studying whether an 8‐week meditation program reduces stress levels in its

Impact of Sleep Duration on Reaction Time

A research lab is investigating how different amounts of sleep affect reaction times measured on a s

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

Impact of Study Aid on Exam Pass Rates

A school collected data on standardized exam pass rates. Among students who used a study aid, 85 out

Machine Failures in a Factory: A Binomial Approach

In a factory setting, each machine fails with a probability of $$0.05$$ on a given day, independentl

Mobile App Daily Engagement

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

Mobile App vs. Printed Pamphlet for Increasing Exercise Duration

A public health organization wants to determine whether a mobile app intervention or a printed pamph

Online Advertisement Click-Through

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

Parental Involvement and Child's Academic Performance Regression Analysis

A study examines the effect of parental involvement (measured in hours per week) on a child's academ

Random Variable Transformation in a Carnival Game

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

Reading Preferences by Genre and Format

A survey was conducted on reading preferences among 300 respondents. The survey collected data on pr

Sampling Distribution of the Sample Mean from a Normal Population

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

Sampling Distribution of the Sample Range

Consider a simulation where samples are drawn from a uniform distribution on the interval $$[0,1]$$.

Simulation in Hypothesis Testing: Generating a Reference Distribution

A researcher employs simulation to generate the sampling distribution of a test statistic under the

Simulation of the Law of Large Numbers in Practice

A simulation is conducted using a biased die that shows a '6' with a probability of $$0.7$$. The die

Standardized Test Strategies and Scores

A standardized test administered to 800 students records the strategy used when unsure of an answer.

Startup Daily Profit Analysis

A startup estimates its daily profit with the following outcomes: a loss of $$200$$ dollars (probabi

Store Customer Satisfaction Survey

A popular retail store conducted a survey to measure customer satisfaction. Out of 120 randomly sele

Student Study Hours and Exam Performance Regression Analysis

A researcher examines the relationship between the number of hours a student studies (x) and their e

Transformation of Payout Values

A game machine produces a random payout $$X$$ with a mean of $5 and a standard deviation of $3. A re

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 =

TV Advertising and Product Demand Regression Analysis

A company analyzes the relationship between TV advertising spending (in thousand dollars) and produc

Understanding the Central Limit Theorem through Simulation

A simulation is performed where samples are drawn from various non-normal populations (for example,

Urban Traffic Volume and Air Quality

City officials are studying the impact of traffic volume on air quality across several neighborhoods

Urban Traffic Volume and Air Quality Regression Analysis

A city planner studies the relationship between daily traffic volume (in thousands of vehicles) and

Weather Impact on Road Conditions

A study of road temperatures under different weather conditions produced the following results. Use

Analyzing Daily Coffee Sales Sampling Distribution

A local coffee shop claims its daily sales (in dollars) are normally distributed with a mean of $$\m

Central Limit Theorem in Transportation: Bus Arrival Times

The delays in bus arrivals in a city are skewed with a mean delay of 8 minutes and a standard deviat

Coffee Bean Package Weight Analysis

A coffee company packages its coffee in bags. The weight of a coffee bag is normally distributed wit

Comparing Durability of Lightbulbs

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

Comparing Sampling Distribution of the Sample Mean in Normal vs. Skewed Populations

Two populations, A and B, both have the same mean $$\mu = 100$$ and standard deviation $$\sigma = 20

Environmental Study: Tree Heights

A biologist is studying tree heights in a forest. Although individual tree heights are not normally

Estimator Comparison for Population Mean

Consider two estimators for a population mean: the sample mean $$\bar{x}$$ and a 10% trimmed mean (w

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

Exploring the Sampling Distribution of a Proportion in Smartphone Ownership

In a survey, it is found that 40% of respondents own a smartphone. A random sample of 200 respondent

Hospital Patient Satisfaction by Department

A hospital surveyed patient satisfaction in three departments. The table below displays the number o

Naked Mole Rat Life Expectancy Study

Naked mole rats have a life expectancy that is approximately normally distributed with a mean of $$2

Normal Approximation for Binomial Proportions

In a large survey, $$65\%$$ of respondents favor a new policy. In a random sample of $$100$$ respond

Online Shopping Behavior: Proportion Analysis

A researcher studying online shopping behavior estimates that 30% of shoppers return items. In a ran

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 Proportions: Political Polls

An exit poll surveys two candidates. Candidate X receives support of 48% from a sample of 400 voters

Sampling Distribution for Sample Means: Energy Drink Caffeine Levels

An energy drink has an average caffeine content of $$\mu = 200$$ mg with a standard deviation of $$\

Sampling Distribution of a Sample Proportion for Disease

In a health study, it is known that 5% of the population has a particular disease. A random sample o

Sampling Distribution of Differences in Proportions

In a study of customer eating habits at two fast‐food restaurants, it was observed that at Restauran

Sampling Distribution of the Maximum: Weather Temperature Extremes

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

Simulation of the 90th Percentile

A study simulates the sampling distribution of the 90th percentile from a non-normal distribution. A

Social Media Use and Sleep Duration

Researchers investigated the impact of social media use on sleep duration. Two independent groups we

Analysis of Emergency Room Wait Times Satisfaction

A hospital surveyed patients about their satisfaction with emergency room wait times. In a sample of

Analyzing Proportions as a Function of Batch Size

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

Assessing Customer Satisfaction in a Retail Store

A retail store surveys 200 customers and finds that 150 are satisfied with their shopping experience

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

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

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 Preference Difference Between Cities

A regional chain surveys customers in two cities regarding their preference for a new product. In Ci

Customer Satisfaction in a Retail Store

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

Customer Satisfaction Survey

A company has collected customer satisfaction data from two sources. In-store customers (Group A) we

Customer Satisfaction: In-Store vs. Online Shoppers

A retail store conducted a survey. Among in-store shoppers, 340 out of 400 reported being satisfied,

Digital Platform Success Rate Comparison

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

Effectiveness of a Drug

A clinical trial is conducted to test the effectiveness of a new drug. In the trial, 400 patients we

Effectiveness of a Social Media Campaign

A company launched a social media campaign to increase brand engagement. Two surveys were conducted:

Environmental Policy Opinion Poll

A survey was conducted to assess public support for a new environmental policy. In an urban area (Gr

Impact of New Educational Program

A school district implemented a new teaching method aimed at improving student performance. In a stu

Implications of Errors in a Safety Inspection

A company's quality control department conducts a safety inspection of a new car model. The manufact

Investigative Analysis of Consumer Behavior

A company undertakes a comprehensive marketing research project to analyze consumer behavior towards

Medical Trial: Comparing Treatment and Control

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

Online Shopping Behavior

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

Product Return Rates by Category

A retail store analyzed product return rates for different categories. Products are classified into

Public Health Confidence Interval

A hospital conducted a simple random sample of 500 patients to gauge satisfaction with treatment qua

Public Health: Influenza Vaccination Rates

A public health study compares influenza vaccination rates between urban and rural areas. In urban a

Public Survey on Recycling: Urban vs. Rural

A public survey investigated recycling habits in two different areas. In an urban area, 180 out of 3

Reading Program Impact Study

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

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

Simulation and Analysis for Rare Diseases

An epidemiologist is studying a rare disease with an estimated prevalence of 0.5%. They simulate dra

Social Media Usage Among Age Groups

A survey on social media usage was conducted among two age groups. Among individuals under 30, 160 o

Traffic Accident Analysis

A study on traffic accidents examined the severity of accidents (Severe vs. Minor) and the driver’s

University Enrollment Statistics

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

Urban vs Rural Voter Support Analysis

A political poll collected data from two independent groups: urban voters and rural voters. In the u

Urban vs. Rural: Survey on Public Transportation Usage

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

Vaccine Acceptance Rates

Researchers want to compare vaccine acceptance between urban and rural populations. In an urban area

Voting by Race

A political science study collected data on voting behavior by race. Voters are classified as either

Voting Patterns on Renewable Energy

A survey was conducted in two states regarding support for renewable energy initiatives. In State X,

Web Advertisement Click-Through Rates

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

Air Quality Measurements: Urban vs. Rural

An environmental scientist is interested in comparing the air quality between an urban area and a ru

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

Coffee Shop Wait Times

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

Delivery Times: Standard vs. Express Shipping

A logistics company wants to compare the average delivery times for its two shipping methods. Data c

Effect of a New Fertilizer on Crop Yield

An agricultural researcher investigates the effect of a new fertilizer on the yield of a particular

Effectiveness of a New Drug

A clinical trial was conducted to determine if a new drug reduces systolic blood pressure. For each

Effectiveness of Drug Treatments

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

Impact of Training Programs on Test Scores

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

Investigating Student Reaction Times

A psychologist studies the reaction times of 30 college students using a computerized test. The meas

Investigative Analysis of Customer Service Performance Metrics

A company collects data on customer service performance across two centers. For a focused study on c

Life Span Analysis of Light Bulbs

A manufacturer claims that its light bulbs have a long lifespan. In a quality test of 15 randomly se

Lifespan of New Light Bulbs

A company tests the lifespan of a new type of light bulb. A random sample of 18 bulbs shows a mean l

Manufacturing Measurement Variability

A quality control procedure involves monitoring the variability in a product's critical dimension us

Manufacturing Process Improvement

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

Mean Gas Mileage Confidence Interval

A car manufacturer wants to estimate the true mean gas mileage of a new model. A random sample of 12

New Coffee Blend and Alertness Test

A beverage company is testing whether a new coffee blend improves alertness by reducing reaction tim

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

Pre- and Post-Intervention Test Score Analysis

An educational researcher wants to evaluate the effect of a new study program on student performance

Pre- and Post-Treatment Blood Pressure Analysis

In a clinical trial, patients' systolic blood pressure is measured before and after a new treatment.

Reaction Time One-Sample t-Test

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

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

Simulating the Effect of Sample Size on Confidence Interval Precision

A statistician performs a simulation study to examine the effect of sample size on the precision of

Simulation of Sampling Distribution for Mean Rainfall Amounts

A meteorologist simulates the sampling distribution of the average daily rainfall (in inches) record

Simulation of Sampling Distribution for Mean Recovery Time

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

Simulation of Sampling Distribution of Mean Reaction Times

In a cognitive psychology study, reaction times (in milliseconds) to a stimulus are collected. A sim

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

Student Participation in Extracurricular Activities

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

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 GPA Analysis

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

Workplace Wellness Program Evaluation

A company evaluates its workplace wellness program by comparing the health outcomes of employees who

Yearly Comparison of Mathematics Test Scores

A school wishes to compare average mathematics test scores between two academic years. The data is s

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

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

Book Genre Popularity Study

A survey by a local library aims to determine if the popularity of book genres matches the library's

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%

Candy Flavor Preferences: Goodness-of-Fit Test

A local candy shop claims that customer preferences for its four candy flavors (chocolate, strawberr

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

Consumer Preference Survey: Chi-Square Goodness-of-Fit

A fast‐food restaurant expects that there is no preference among four new burger flavors. To test th

Customer Satisfaction Survey Across Store Locations

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

Distribution of Types of Crimes in a City

A study compares the types of crimes in two districts of a city. District A reported: Property = 80,

Drug Side Effects Analysis: Chi-Square Test for Independence

In a controlled clinical trial, researchers are investigating whether the frequency of certain side

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

Examining Health Outcomes by Smoking Status

Researchers are interested in determining if there is an association between smoking status and heal

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,

Extracurricular Participation and Academic Performance Independence Test

A survey of high school students collected data on extracurricular activity participation (Yes, No)

Fair Dice Rolling Goodness-of-Fit Test

A die is believed to be fair. In 120 rolls, the outcomes were observed as follows: Face 1 = 14, Face

FRQ 2: Association Between Smoking Behavior and Gender

A public health survey collected data on smoking status and gender from 150 individuals. The observe

FRQ 9: Student Enrollment Preferences Across Tracks

A high school offers four different tracks: STEM, Humanities, Arts, and Vocational. The school expec

FRQ 17: Customer Complaint Types and Resolution Outcomes

A company categorizes customer complaints into three types: Billing, Service, and Product Quality. E

FRQ 18: Evaluating Distribution of Blood Types in a Sample Population

A hospital expects the distribution of blood types in the general population to be: Type O: 45%, Typ

Genetic Ratios in Plant Breeding – Chi-Square Goodness-of-Fit

In a plant breeding experiment, a dominant-recessive trait is expected to follow a 3:1 phenotypic ra

Job Satisfaction Across Departments: Chi-Square Test for Homogeneity

An organization wants to compare job satisfaction among employees in three different departments: Sa

Marketing Strategy Effectiveness

A company wants to assess if customer responses vary by the type of advertisement. Three ad types (O

Preferred Payment Methods: Chi-Square Test for Homogeneity

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

Restaurant Menu Distribution Analysis

A popular restaurant chain claims that the distribution of orders among four cuisine types (Italian,

Robustness of Chi-Square Test: Small Expected Counts

A survey on elective subject choice among students produced observed counts: Subject A = 25, Subject

Simulating the Distribution of the Chi-Square Statistic

A researcher wishes to use simulation to approximate the sampling distribution of the chi-square sta

Smartphone Brand Market Share: Goodness-of-Fit Test

A survey of 200 smartphone users records their preferred brand among four brands: A, B, C, and D. Th

Species Distribution in Habitats: Chi-Square Goodness-of-Fit

A wildlife researcher hypothesizes that a species is distributed among four habitat types in a fixed

Survey on Preferred Modes of Transportation

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

Voting Methods: Chi-Square Goodness-of-Fit

In a local election, voters could choose from three voting methods: In-person, Mail-in, and Online.

Advertising Data: Predicting Sales

A company wants to study how advertising spending (x, in thousands of dollars) affects product sales

Coffee Consumption and Alertness

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

Crop Yields and Fertilizer Usage

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

Customer Satisfaction and Wait Times

A restaurant chain surveyed 50 customers to study the effect of wait time (x, in minutes) on satisfa

Diet Plans and Weight Loss

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

Dosage-Response in Drug Trials Simulation

A clinical researcher investigates the effect of drug dosage (in mg) on patient response scores. To

Electricity Usage and Temperature

An energy analyst examines how average daily temperature (x, in °F) affects household electricity us

Exercise Duration and Weight Loss

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

Exercise Duration vs Heart Rate

A fitness researcher analyzed the relationship between exercise duration (in minutes) and heart rate

Impact of Teaching Methods on Math Performance

A school district is interested in determining whether a new teaching method improves performance on

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

Online Engagement and Sales Conversion

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

Predicting Ice Cream Sales from Temperature

In a study of 25 summer days, data were collected on daily maximum temperature (x, in °F) and ice cr

Rainfall vs Crop Yield

An agricultural economist is investigating the relationship between annual rainfall (in inches) and

Reaction Rate in Chemistry: Temperature and Reaction Time

An experiment investigates the effect of temperature (x, in °C) on reaction time (y, in seconds). Da

Student Performance and Study Hours

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

Temperature and Electricity Consumption

A power company studies the relationship between daily average temperature (in °C) and electricity c

Water Usage and Crop Yield

An agricultural scientist is studying the relationship between water usage (in cubic meters per acre

Weekly Internet Hours vs Exam Score Improvement

An education researcher collected data on the number of weekly hours students spent on the internet

Weight Loss and Diet Adherence

A nutritionist is studying the relationship between the number of diet counseling sessions attended

Wind Speed vs Power Output

An energy analyst is exploring the effect of wind speed (in m/s) on the power output (in kilowatts)