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

Analyzing Z-Scores and Normal Distribution

Assume that a particular set of data is normally distributed with a mean of 100 and a standard devia

Basketball Free Throw Percentage Confidence Interval

A basketball player takes 80 free throws and makes 60 of them. Answer the following parts:

BMI and Blood Pressure Regression Analysis

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

Boxplot Construction from Exam Scores

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

Categorical Data Analysis: Survey on Preferred School Year Length

A survey of 2000 parents asked about their preference for the length of the school year. The respons

Cumulative Frequency Analysis of Age Distribution

A study compares the age distributions of two different years using cumulative frequency plots. In Y

Customer Service Call Duration

Customer service call durations are approximately normally distributed with a mean of $$8$$ minutes

Effects of Multiplicative Transformations on Test Scores

A data set representing test scores is given as follows: {45, 55, 67, 73, 82, 88, 90}. Answer the fo

Employee Salary Adjustments

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

Event Attendance by Invitation Type

An event organizer tracked attendance based on invitation type (Digital, Paper) and the outcome (Att

Home Run Distances in Ballparks

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

Impact of an Outlier on Summary Statistics

Consider the data set: {22, 25, 27, 30, 32, 150}, where the value 150 is a potential outlier. Answer

Interquartile Range and Boxplot Construction

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

Investigative Analysis of Public Health Survey on COVID-19

A public health survey was conducted with 500 adults to assess COVID-19 vaccination status, experien

Machine Reliability Testing

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

Marketing Campaign Reach by Region

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

NBA Team Wins: Distribution Assessment

The numbers of wins for NBA teams in two conferences are summarized using comparative data displays.

NBA Wins: Analyzing Back-to-Back Stem Plots

A back-to-back stem plot displays the number of wins for NBA teams from the Eastern and Western Conf

Product Return Rates Across Regions

A company tracks product returns across four regions (North, South, East, West) with outcomes 'Retur

Public Transportation Usage by Occupation

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

Salary Analysis: Effect of Raises on Mean Salary

A company has six employees whose current salaries are $$3000$$, $$7000$$, $$15000$$, $$22000$$, $$2

Simulation of the Sampling Distribution of the Mean Number of AP Classes Taken

A study of 2200 high school seniors reports the number of AP classes taken as follows: 0 AP classes

Social Media Engagement Analysis

A social media post is viewed by 200 users, and each user independently has a 5% chance of liking th

Stemplot Construction: Analyzing a Data Set

A dataset of 11 numbers is provided as follows: {12, 15, 15, 17, 17, 18, 20, 22, 22, 23, 25}.

Temperature and Reaction Rate Regression

A chemical kinetics experiment measured the reaction rate (in mol/sec) at different temperatures (in

Treatment Outcomes in Hospital Study

A hospital conducted a study on two treatments (Treatment X and Treatment Y) to evaluate patient out

Unit Conversion Impact on Summary Statistics

A data set representing the lengths of objects is given in inches: {12, 24, 36, 48, 60}. Answer the

Advertising Campaign and Sales Analysis

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

Bootstrap Simulation for the Regression Intercept's Sampling Distribution

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

Calculation of Correlation and Linear Regression from Summary Statistics

A study examines the relationship between daily device usage (in hours, X) and a productivity score

Coffee Shop Drink Preference

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

Constructing a Contingency Table from Raw Data

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

Correlation and Coefficient of Determination in Exam Performance

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

Customer Satisfaction Survey

A retail store surveyed customers regarding their visit frequency (Frequent vs. Infrequent) and over

Customer Service and Order Mode Inference

In a survey at a local restaurant, 70 customers ordered online and 30 ordered in-person. Among the o

Effect of Advertisement Frequency on Brand Recognition

A marketing study was conducted to analyze the relationship between the number of advertisements see

Effectiveness of a New Curriculum

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

Environmental Study: Air Pollution vs. Respiratory Issues

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

Environmental Study: Temperature and Ice Cream Sales

An environmental study tracked ice cream sales (in hundreds of dollars) and the daily high temperatu

Evaluating Housing Market Trends Through Transformation

A real estate analyst studies the relationship between house square footage (x) and sale price (y, i

Experience and Salary: Exploring a Nonlinear Relationship

An HR department collects data on the number of years of experience (x) and annual salary (in thousa

Fitness Program Enrollment

A local gym evaluated enrollment trends by comparing two program types (Yoga vs. CrossFit) and atten

Impact of Study Environment on Academic Achievement

A survey of 100 students collected data on their study environment (categorized as 'Quiet' or 'Noisy

Job Training and Post-Training Wages

A job training program collected data from 30 participants on the number of training hours (x) and p

Manufacturing Defects in Two Production Lines

A manufacturing company operates two production lines. A quality control inspection was performed on

Online Learning Preferences

A survey was conducted among 200 students to determine their preferences for online learning. Studen

Simulating the Sampling Distribution of the Sample Mean in Bivariate Data

A study collects data on the number of study hours (x) and exam scores (y) for 100 students. Researc

Simulation of Bivariate Data with Varying Leverage Effects on Regression Coefficients

A researcher simulates bivariate data to explore how the presence of high-leverage points affects th

Simulation of the Impact of Measurement Error on the Sampling Distribution of Pearson's r

A study measures the relationship between two variables, but with varying degrees of measurement err

Temperature and Ice Cream Sales

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

Analysis of Boxplots from an Experiment on Pulse Rates

Researchers conducted an experiment comparing the effects of three beverages (coffee, caffeinated co

Commute Time and Job Satisfaction

A consulting firm conducts a study to examine whether longer commute times (in minutes, x) are assoc

Comparing Treatment Efficacy in a Retrospective Study

A retrospective observational study was conducted to examine the efficacy of two treatments for a pa

Customer Feedback for a New Product

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

Data Collection in a Prospective Observational Study

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

Designing a Prospective Study for a Drug Trial

A pharmaceutical company is testing a new drug for lowering blood pressure. The study will involve f

Diet, Weight Loss, and Regression Analysis

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

Evaluating Bias in a Sampling Process: Voluntary Survey

A city council conducts a voluntary online survey regarding community safety. Out of 150 responses,

Impact of a New Diet on Blood Pressure

A health clinic is investigating whether a new diet can reduce systolic blood pressure. Patients are

Impact of Advertising on Sales Revenue

A chain of retail stores seeks to understand the relationship between advertising expenditures (in $

Internet Usage and Education Level

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

Interpreting Observational Study Data on Exercise and Blood Pressure

A study tracks daily exercise minutes and resulting changes in blood pressure for 100 adults over a

Matched Pairs Design in Educational Research

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

Physical Activity and Cognitive Function in Older Adults

Researchers are investigating whether increased physical activity is associated with better cognitiv

Remote Learning Effectiveness

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

Replication in Experimental Designs: Water Purification Study

Researchers are testing various water purification techniques in an experimental study. Replication

Simulating Sampling Distributions for Quality Control in Manufacturing

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

Systematic Sampling in a Traffic Accident Study

A city transportation department wants to assess the frequency of traffic accidents at intersections

Teaching Methods and Student Performance

A school wants to compare the effectiveness of two different teaching methods on student performance

Urban Green Spaces and Air Quality

An urban planning study is being conducted to determine whether proximity to green spaces is associa

Voting Preference Analysis

A political analyst collected data on voting preferences by age group. The table below shows the num

Carnival Game Payoff Transformation

In a carnival game, the payoffs are: $$2$$ dollars with probability $$0.5$$, $$5$$ dollars with prob

Casino Chips: Sum and Variance Calculation

At a casino, couples receive free chips by drawing a card from two bags. One bag (X) contains the va

City Traffic Speed Analysis

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

Comparing Consumer Spending at Two Malls

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

Comparing Daily Step Counts: Traditional Pedometer vs Fitness Tracker

A study compared the daily step counts of two groups: one group used a traditional pedometer (n = 50

Comparing Manufacturing Processes for Defect Reduction

An industrial engineer is comparing two manufacturing processes to determine which one produces fewe

Defect Rate Comparison between Two Factories

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

Drug Effectiveness Study

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

Effects of Outliers on Sampling Distributions

A simulation study involves drawing samples from a dataset that contains outliers. For each sample,

Employee Training and Department Performance

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

Exam Score Cumulative Distribution

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

First Honest Encounter: Geometric Distribution

In ancient Greece, suppose only 12% of men are honest. Let \(X\) represent the trial on which the fi

Hospital ER Wait Times

A hospital is interested in assessing the average wait time in its emergency room. In a random sampl

Impact of Study Habits on Test Scores

A teacher wants to examine if spending an extra 30 minutes reviewing material after class influences

Investigative Study on Public Health Intervention

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

Raffle Ticket Payouts in a Fundraiser

A charity raffle sells 500 tickets at $2 each. There is one main prize of $800 and two smaller prize

Rare Defects and Poisson Approximation

A factory produces electronic components with a defect rate of 0.002. In a shipment of 2000 units, l

Retail Customer Purchases: Random Variable Analysis

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

Sampling Distribution of the Sample Mean from a Normal Population

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

Social Media Usage Patterns by Age Group

A study surveyed 300 social media users to determine their preferred platform. The respondents were

Student Study Hours and Exam Performance Regression Analysis

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

Student Testing Strategy and Scores Analysis

A standardized literacy test consists of 100 multiple-choice questions. When uncertain, test takers

Suit Name Letter Count

A card is drawn from a standard 52-card deck. Let the random variable $$X$$ be the number of letters

Survey Response Binomial Analysis

In a survey of $$50$$ respondents, each respondent has a $$0.65$$ probability of giving a positive r

The Impact of Sample Size on Outcome Predictability

A game organizer is designing a carnival game that involves tossing a fair coin. A player wins if th

Voter Turnout in Two Cities

A researcher collected data on the number of people who voted in two cities during an election. In C

Bacterial Count in Water Samples

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

Biased Estimator in Quality Control

A manufacturer uses an estimator to measure the maximum strength of a new material. A simulation of

Caffeine Content Analysis in Energy Drink Boxes

An energy drink contains caffeine distributed with a mean of 200 mg and a standard deviation of 10 m

Central Limit Theorem in Action: Distribution of Household Incomes

In a large metropolitan area, household incomes are highly skewed. A research team takes repeated ra

Central Limit Theorem in Customer Service Times

In a call center, individual call durations are skewed with an average of $$\mu = 5$$ minutes and a

Comparing Mean Reaction Times Between Two Groups

A psychological study compares reaction times under two conditions. Group A (n = 40) has a mean reac

Confidence Interval and Sampling Distribution in Height Estimation

A researcher aims to estimate the average height of college students with a margin of error of $$1$$

Effect of New Teaching Method on Student Scores

A school district is testing a new teaching method. Two groups of students are studied: a control gr

Effect of Restaurant Remodel on Customer Behavior

A fast-food restaurant tested whether remodeling their premises had an effect on how much food custo

Employment Benefits Perception

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

Environmental Concerns by Community Type

A survey was conducted to assess environmental concerns among residents in different community types

Evaluating Sample Proportions in a Survey

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

Financial Returns: Biased vs. Unbiased Estimators

Investment analysts use two estimators to predict the expected return of a financial asset. Estimato

Genetic Mutations in New Fathers

A study estimates that 40-year-old men contribute an average of $$65$$ genetic mutations (with a sta

Hospital Patient Satisfaction by Department

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

Lightbulb Life Expectancy Analysis

A particular brand of lightbulb has a lifespan that is approximately normally distributed with a mea

Lightbulb Life Expectancy Analysis

A certain brand of lightbulbs has a life expectancy that is approximately normally distributed with

Naked Mole Rat Life Expectancy Study

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

Quality Control in Manufacturing: CLT Application

A manufacturing plant produces metal rods whose lengths are not normally distributed, but have a pop

Sampling Distribution for Sample Means: Caffeine Content in Energy Drinks

An energy drink has its caffeine content normally distributed with a mean of $$\mu = 200$$ mg and a

Sampling Distribution for Sample Means: Energy Drink Caffeine Levels

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

Sampling Distribution for Sample Proportions in Math Anxiety Study

A recent study estimates that 80% of people with high math anxiety experience brain activity similar

Simulation and Empirical Distribution: Study Habits

A researcher collects data on weekly study hours for high school students. In an initial sample of 1

Sports Performance Data Analysis - Batting Averages

In a baseball league, the average batting average is 0.280 with a standard deviation of 0.030. A coa

Student Performance and Study Techniques

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

Widget Lifespan Quality Control

A factory produces widgets with an average lifespan of $$500$$ hours and a standard deviation of $$2

Advertising Impact on Brand Recognition

A company launched an advertising campaign in two regions. In Region 1, a post-campaign survey of 50

Analysis of Survey Data on Online Learning

A survey of 150 students indicates that 90 prefer online learning. A table summarizing the responses

Coffee Shop Loyalty

A coffee shop chain is investigating customer loyalty. A survey at the downtown branch (Group A) sam

Comparing Defect Rates in Two Factories

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

Comparing Satisfaction Between Two Stores

A retail chain wants to compare customer satisfaction between two of its stores. In Store A, 150 cus

Customer Preference Difference Between Cities

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

Customer Satisfaction in a Retail Store

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

Diet Choices by Gender

A survey was conducted to analyze diet choices among male and female participants. Participants were

Epidemiology Study: Difference in Disease Incidence

An epidemiological study examines disease incidence in two groups. In the exposed group (n = 400), t

Evaluating Strike Support

A union conducted a survey among 125 members to decide on whether to support a strike. In the survey

Factory Quality Control Analysis

In a factory, quality control is carried out by inspecting a sample of items. Out of 800 items inspe

Government Policy Approval Confidence Interval

A polling organization surveyed 800 voters to measure the approval of a recent government policy. Am

Hypothesis Testing for Brand Satisfaction

A company claims that 85% of its consumers are satisfied with its product. A random survey of 200 cu

Interpreting a Confidence Interval

A study on dietary habits produces a 95% confidence interval for the proportion of adults consuming

Job Satisfaction by Shift Work

A hospital survey examined job satisfaction among nurses working on the Day Shift and the Night Shif

Medical Trial: Comparing Treatment and Control

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

Online Education Satisfaction

A study comparing satisfaction with education methods surveyed two groups. One group of online stude

Political Campaign Support Analysis

A political campaign conducted a survey to determine support for a candidate. In the survey, a simpl

Political Opinion Poll Analysis

A political poll was conducted to assess support for a proposed tax bill. In a simple random sample

Political Polling: Candidate Approval

Two independent polls were conducted to assess approval ratings for a political candidate. Poll 1, s

Public Library Usage Survey

A city council conducted a survey to determine the proportion of residents using the public library.

Research on Smoking Cessation Program

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

Simulation and Analysis for Rare Diseases

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

Smartphone Brand Preference by Income Level

A market research survey categorized respondents by income level and their preferred smartphone bran

Social Media Campaign Engagement Analysis

A company runs a social media campaign aiming for a target engagement rate of 40%. In a sample of 60

Social Media Influence Study

A marketing firm is investigating whether exposure to a popular social media influencer affects the

Testing for Change in Voter Intent Over Time

An exit poll conducted before and after a major debate shows different levels of support for Candida

University Enrollment Statistics

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

University Policy Support Analysis

A university claims that 60% of its students support a proposed policy change. A random sample of 20

Urban vs. Rural: Survey on Public Transportation Usage

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

Website A/B Testing

An online retailer is testing two versions of its webpage (Version A and Version B) to determine whi

Advertising Budget and Sales Performance Analysis

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

Analysis of Weekly Exercise Duration

A wellness program is designed to increase weekly exercise time. In a sample of 16 participants unde

Change in Manufacturing Process: Product Lifespan

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

Comparing New Drug Efficacy

A pharmaceutical study compares two medications for lowering blood pressure. Group 1 (Drug A) consis

Comparing Two Diets

A nutritionist compares the effects of two diets on weight loss. In a study, Diet 1 (n = 30) results

Customer Satisfaction at Two Store Branches

A retail chain collects customer satisfaction ratings (on a scale of 1 to 10) from two store branche

Customer Satisfaction Survey

A popular online retailer claims an average customer satisfaction rating of 8.5 (on a 10-point scale

Daily Steps: Wearable Device Analysis

A fitness tracker company wishes to estimate the average number of steps taken per day by its users.

Delivery Times: Standard vs. Express Shipping

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

Detection of Production Process Anomalies via Simulation

A factory monitors its production process by measuring the deviation from a target product dimension

Effectiveness of a New Drug

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

Effectiveness of Drug Treatments

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

Election Polling Power Analysis

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

Employee Productivity Analysis

A study compares employee productivity scores between two departments. Department 1 (n = 30) has a s

Employee Training Effectiveness

A company conducts a study to evaluate the effectiveness of a new training program. The program's im

Evaluating a Mobile App's Impact on Daily Step Count

A health technology firm develops a new mobile application aimed at increasing daily physical activi

Examining Teaching Methods

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

Fuel Consumption and Distance Traveled Analysis

The scatterplot below displays data on the gallons of fuel used (x-axis) and the corresponding dista

Impact of New Traffic Signals on Commute Times

A city installs new traffic signals at a busy intersection to improve traffic flow. Traffic engineer

Life Span Analysis of Light Bulbs

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

Lifespan of New Light Bulbs

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

Medical Device Response Time Analysis

A study is carried out to evaluate the response time (in seconds) of a new medical device. A random

New Coffee Blend and Alertness Test

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

Plant Growth under Different Fertilizers

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

Reaction Time Hypothesis Test

A psychologist wishes to test a manufacturer's claim that the average driver reaction time is \(0.8\

SAT Preparation Class Improvement

A tutor runs an SAT preparation class with 25 students. The differences between the post-test and pr

Simulation from a Bimodal Population

A researcher is studying a population that exhibits a bimodal distribution (e.g., test scores from t

Simulation of Sampling Distribution for Average Household Income

An economist is studying household incomes, which are known to be right-skewed. The economist uses s

Simulation of Sampling Distribution of Mean Reaction Times

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

Social Media Usage Before and After an Intervention

A researcher studies the effect of a digital detox program on daily hours spent on social media. For

Weight Loss Confidence Interval

A nutritionist is studying the effectiveness of a new weight loss program. A random sample of 20 par

Weight Reduction Program Evaluation

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

Wind Speed Measurements: Station Upgrade Impact

A weather station upgrades its sensors and collects paired wind speed measurements from before and a

Animal Species Distribution in Habitats: Chi-Square Test

Researchers collected counts of three animal species (Deer, Rabbit, Fox) in two habitats. The counts

Customer Satisfaction Ratings Across Service Centers

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

Diet Preference Among Athletes

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

Drinking Habits and Health Outcomes: Test for Independence

A health study surveys 300 individuals, recording their drinking habits (Never, Occasionally, Regula

Drug Side Effects Analysis: Chi-Square Test for Independence

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

Education Level and Internet Usage Frequency – Chi-Square Test for Independence

A survey of 500 individuals collected data on their education level (High School, Bachelor's, Master

Effectiveness of a New Training Program across Branches

A company implements a new training program in three of its branches. After the program, employees a

Election Polls: Goodness-of-Fit for Candidate Support Ratios

In a local election survey of 500 voters, the observed support percentages for candidates were: Cand

Evaluating Student Performance: Chi-Square Goodness-of-Fit in Grades Distribution

A large high school believes that the distribution of final letter grades (A, B, C, D, F) on a stand

Fair Dice Rolling Goodness-of-Fit Test

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

FRQ 1: Distribution of Customer Preference for a New Snack

A snack company claims that the preferences for flavors of its new snack follow the proportions: Fla

FRQ 2: Association Between Smoking Behavior and Gender

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

FRQ 3: Voter Preferences by Age Group: A Homogeneity Test

A study categorizes voters into three age groups (Young, Middle, Older) and records whether they sup

FRQ 8: Sports Participation and Academic Performance

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

FRQ 9: Student Enrollment Preferences Across Tracks

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

FRQ 12: Employee Training Program and Job Promotion

A company is investigating the effectiveness of its training program on job promotions. The collecte

Genetics Research: Rat Coat Colors

In a genetics experiment, the expected Mendelian ratio for rat coat colors is 3:1 (dominant: recessi

Goodness-of-Fit Test for Web Traffic Sources

A website manager expects that web traffic comes from four sources with the following proportions: D

Independence of Smoking and Lung Disease

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

Production Line Defect Rates Homogeneity Test

A factory operates four production lines, each producing a sample of 200 items. The numbers of defec

Quality Control Across Production Lines – Chi-Square Test for Homogeneity

A company monitors the quality of items produced by three production lines. In monthly samples of 15

Race Participation in Marathon

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

Shopping Behavior: Online vs. In-store by Age Group

Researchers want to examine if shopping mode (Online vs. In-store) is related to age group. The surv

Smartphone Brand Market Share: Goodness-of-Fit Test

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

Social Media Platform Usage

A marketing agency expects that among 500 consumers, the usage of social media platforms is distribu

Teacher Satisfaction by Department: Chi-Square Test for Homogeneity

A school district wishes to determine if job satisfaction among teachers varies by department (Math,

Teaching Methods Effectiveness: Homogeneity Test

An educational study compares the effectiveness of three teaching methods (Method 1, Method 2, Metho

Traffic Light Malfunction Analysis

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

Transportation Mode Among City Residents

A city survey examines the relationship between type of residence (Urban vs. Suburban) and preferred

Type of Transportation and Commute Satisfaction

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

Advertising Budget and Sales Revenue

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

Advertising Spend and Website Traffic

A company analyzed how its weekly advertising spend (in thousands of dollars) influences website tra

Agricultural Yield Analysis

Agricultural scientists examine the effect of fertilizer application (in kg/ha) on crop yield (in to

Air Quality and Traffic Flow

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

Biking Speed and Heart Rate

A sports scientist is investigating the relationship between average biking speed (in mph) during ex

Coffee Consumption and Alertness

Researchers are investigating the relationship between the number of cups of coffee consumed per day

Coffee Consumption and Alertness

A researcher investigated the relationship between daily coffee consumption (measured in cups) and a

Coffee Consumption and Anxiety Levels

A psychologist investigates whether there is a relationship between the number of cups of coffee con

Crop Yield and Fertilizer Application

An agronomist is examining how the amount of fertilizer applied (x, in kg) affects crop yield (y, in

Effect of Class Size on Student Achievement

An education researcher examines data from 50 classrooms to study the relationship between class siz

Effects of Weather on Tourist Visits

The city tourism board collected data to study the relationship between daily high temperature (in °

Electricity Bill vs Temperature

A utility company studied the relationship between the average monthly temperature (in $$^\circ F$$)

Engine Size vs Highway Fuel Efficiency

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

Engine Temperature and Efficiency Loss

An engineering study investigates the effect of engine temperature ($$x$$, in $$^\circ C$$) on effic

Engineering: Stress and Strain in Alloys

In an experiment studying a new alloy, engineers measured stress (x, in MPa) and strain (y, dimensio

Environmental Study: Pollutant Concentration and Respiratory Issue Rates

Researchers are studying the impact of pollutant concentration (in parts per million, ppm) on the ra

Impact of Workout Hours on Body Fat Percentage

A fitness study collected data on the number of hours individuals work out per week (x) and their bo

Modeling Blood Pressure Response to Medication Dosage

A medical study investigates the effect of medication dosage (x, in mg) on the reduction in systolic

Practice Time and Music Performance Skill

A study investigates the effect of weekly practice hours ($$x$$) on a music performance skill score

Predicting Sales Based on Advertising Budget

A company wants to understand the relationship between its advertising spending (in thousands of dol

Predicting Student Performance with Attendance Rates

A teacher collects data on student attendance rates (x, in percentage) and corresponding performance

Rainfall and Crop Yield

An agricultural study investigates the relationship between total rainfall (in inches) during the gr

Reaction Rate in Chemistry: Temperature and Reaction Time

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

Relationship Between Stress Level and Reaction Time

A psychological experiment collected data on stress levels (x, on a scale of 0-100) and reaction tim

Sleep Hours and Cognitive Performance

A study examines the effect of sleep hours (x) on cognitive performance (y, measured as a test score

Social Media Advertising and Customer Clicks

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

Social Media Influence on Product Sales Simulation

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

Speed and Fuel Efficiency

A study examines the relationship between vehicle speed ($$x$$, in mph) and fuel efficiency ($$y$$,

Student Performance and Attendance

A school administrator wants to understand the relationship between class attendance and test scores

Student Study Hours and Exam Scores Simulation

A high school teacher is interested in how the number of hours spent studying affects exam scores. T

Temperature Effect on Ice Cream Sales

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

Weight Loss and Diet Adherence

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