AP Statistics FRQ Room

Analyzing Cumulative Frequency and Percentiles from Exam Scores

The cumulative frequency table below summarizes the scores on an exam for a class of 100 students:

Analyzing z-Scores from a Frequency Distribution

The following table displays z-scores along with their corresponding cumulative percentile rankings

AP Class Enrollment Analysis

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

Cafeteria Food Satisfaction Proportion

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

Comparing Exam Score Distributions

Two classes took the same exam and their performances are summarized with back-to-back stemplots. Al

Customer Satisfaction in Retail Chain

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

Effect of Fertilizer Types on Tomato Yield

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

Effect of Outliers on the Sampling Distribution of the Mean

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

Investigating Class Test Scores

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

Nutrition Study: Effects of Diet on Weight Loss

A nutritionist intends to study whether different diets lead to different average weight losses over

Political Affiliation and Media Consumption

A study surveyed 300 voters on their political affiliation (Party A, Party B, Independent) and their

Political Polling: Candidate Preference

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

Rainfall Occurrence: Binomial Model

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

Relative Frequency Calculation from Pet Ownership Survey

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

Restaurant Preference and Time Slot

A survey of 200 diners asked about their restaurant choice (Restaurant A or Restaurant B) and the ti

Restaurant Wait Time Analysis

A consumer group claims that a certain fast-food restaurant’s average wait time is 4 minutes. They c

Simulated Sampling Distribution of the Standard Deviation

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

Sleep Deprivation and Reaction Times

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

Stock Price Outlier Analysis

Consider the summarized daily stock prices (in dollars) of a company given by the following five-num

Survey of Smartphone Usage Time

A survey of 500 students categorized their daily smartphone usage (in hours) with the following data

Voting Behavior by Education Level

A political survey collected data on voters' education level (High School, College, Graduate) and th

Analysis of Marketing Campaign Data: Sales vs. Advertisements

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

Art Exposure and Creativity Scores

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

Attendance and Test Performance

A teacher collected data from 25 classes on average class attendance (in %) and average test scores

Bootstrapping Confidence Interval for Regression Slope

A small study examines the relationship between annual income (x, in $1000s) and self-reported happi

Call Duration Analysis in a Service Center

In a call center, call durations (in minutes) are normally distributed with a mean of $$3$$ minutes

City Bicycle Usage Study

A city bike‐share program collected data on daily high temperatures (in °F) and the total number of

Comparing Effectiveness of Educational Workshops

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

Constructing a Scatterplot from Given Data

The following table lists paired observations of variables x and y. | x | y | |----|----| | 5 |

Customer Satisfaction and Purchase Frequency

A retail store surveyed 80 customers and found that the satisfaction rating (on a scale of 1-10) pre

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 Tracker Analysis

A fitness center collected data from individuals using fitness trackers, recording daily steps (x) a

Impact of Caffeine Intake on Reaction Time

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

Impact of Study Methods on Test Performance

A university is interested in determining the effect of different study methods on students' perform

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

Online Course Enrollment Prediction

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

Online Ratings and Restaurant Revenue

A restaurant chain collected data on their average online rating (x, on a 5‐point scale) and corresp

Pets and Stress Levels

A study investigated the relationship between the number of pets owned (x) and self-reported stress

Predicting Fitness Improvement from Exercise Duration

A fitness study examined the relationship between the daily exercise duration (x, in minutes) and th

Residual Plot Analysis for a Blood Pressure Study

A medical study uses a regression model to predict blood pressure (Y) from sodium intake (X). The re

Study Habits and Exam Scores: Regression Inference

A study of 30 students collects data on hours studied (x) and exam score (y). The regression analysi

Temperature and Ice Cream Sales

An ice cream vendor records daily maximum temperatures (in degrees Fahrenheit) and the number of box

Urban Noise and Sleep Quality Study

A study investigated the impact of urban noise level (measured in decibels, x) on individuals' self‐

Voting Behavior and Media Consumption

A political analyst surveyed 300 individuals to study the relationship between media consumption and

Analysis of Recycling Behavior

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

Analyzing Bias in Convenience Sampling at a Mall

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

Analyzing the Effect of Study Habits on SAT Scores

A study compared SAT scores of two groups of students. The group using flashcards (Group F) had 50 s

Community Fitness Program and Weight Loss

A local government launches a community fitness program to help residents lose weight. The program i

Commute Time and Job Satisfaction

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

Comparing Disease Incidence in Two Regions

A public health study investigated the incidence of a particular disease in two regions. In Region A

Comparing Prospective and Retrospective Data Collection in Education Studies

A school district wants to study the impact of extracurricular activities on academic performance. T

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

Designing a Prospective Study on Exercise and Stress Reduction

A local fitness center aims to study the impact of a new exercise regimen on reducing stress levels

Effect of Sleep Duration on Reaction Time

In an experimental study on college students, the relationship between sleep duration (in hours, x)

Effectiveness of Stress Reduction Methods: Yoga vs. Meditation

A wellness center studied the effectiveness of yoga and meditation on reducing stress. In the yoga g

Effects of Diet Programs on Weight Loss

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

Efficacy of a Mobile App for Tracking Physical Activity

A study compared the effectiveness of a mobile app in helping users meet their daily step goals. In

Environmental Study on Pollution Levels

A retrospective study examined water quality from 40 rivers in a region, measuring the concentration

Evaluating a New Teaching Method

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

Evaluating Bias in Voluntary Response Surveys

A local government agency conducts a survey on community satisfaction with public transportation thr

Evaluating the Effectiveness of a New Drug

A clinical trial compared a new drug with a placebo regarding patient recovery. The data are summari

Film Ratings Analysis

A movie review aggregator collects ratings on a scale from 1 to 10 from a simple random sample of 80

Impact of Advertising on Sales Increase

A company wants to evaluate if exposure to an advertising campaign affects the likelihood of an incr

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

Investigating Response Time in Emergency Calls

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

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

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

Matched Pairs Design in Educational Research

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

Observational Study Versus Experiment in Healthcare

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

Predicting Car Mileage from Engine Size

A study of 80 cars investigates the relationship between engine size (in liters, x) and fuel efficie

Public Health Intervention on Smoking Cessation

A city public health department wants to evaluate the effectiveness of a new anti-smoking campaign i

Randomized Controlled Trial: Vaccine Efficacy

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

Remote Learning Effectiveness

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

Replication in an Agricultural Experiment

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

Retail Customer Purchase Binomial Model

A retailer estimates that the probability of a customer making a purchase during a visit is 10%. On

Retail Store Checkout Efficiency Study

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

Retrospective Versus Prospective Public Health Studies

A public health agency is planning to study the spread of a novel pathogen. They have access to exte

Salesperson Success: Geometric Probability

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

Sampling Distribution in Voter Polling

A polling organization is estimating the approval rating for a political candidate. Suppose the true

Scatterplot Analysis and Regression Line Interpretation

A researcher investigates the relationship between the number of hours studied (x) and exam scores (

Simulating Cluster Sampling and its Effects on the Sampling Distribution

A health survey is conducted using cluster sampling by selecting several schools from a district and

Simulation of the Sampling Distribution of Proportions in Quality Testing

A factory produces light bulbs and each bulb is classified as defective or nondefective. A simulatio

Social Media Usage among Teenagers

A survey of teenagers collected data on social media platform preferences (Instagram, Snapchat, TikT

Social Media Usage and Mental Health

Researchers are studying the impact of social media usage on mental health among teenagers. A survey

Systematic Sampling in a Traffic Accident Study

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

Temperature and Ice Cream Sales: A Summer Analysis

During the summer, a study was undertaken to analyze whether higher daily temperatures increase ice

Work-from-Home vs. In-Office Job Satisfaction

A human resources study surveyed job satisfaction among employees working from home and those workin

Applying Chebyshev's Inequality in Quality Control

A production process yields items with an average weight of 50 grams and a standard deviation of 5 g

Assessing the Impact of a New Advertisement Campaign

A retail company wants to measure the effect of a new advertisement campaign on store sales. A sampl

Bootstrap Sampling Distribution of the Sample Mean

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

Car Purchase Decisions by Region

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

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

Charity Lottery Expected Outcome

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

Charity Lottery Expected Value Calculation

A charity holds a lottery selling 10,000 tickets at $$1$$ each. One ticket wins a prize of $$7500$$.

Coffee Consumption and Alertness Level Regression Analysis

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

Coin Flip Game Strategies

In a game show, contestants face two different coin flip challenges. In Challenge A, you win if the

Cumulative Distribution Analysis of AP Exam Scores

The following table shows the distribution of scores on an AP Statistics exam:

Daily Steps and Calorie Burn Regression Analysis

A fitness study examines the relationship between the number of daily steps (in thousands) and calor

Defective Lightbulbs: A Binomial Distribution Problem

A lightbulb has a $$0.1$$ probability of being defective, and the outcomes are independent. Analyze

Employee Training and Department Performance

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

Exercise Time and Cholesterol Level Regression Analysis

A health study examining the effect of weekly exercise on cholesterol levels among 80 adults produce

Fuel Efficiency Comparison between Two Vehicle Models

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

Highway Construction Productivity Analysis

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

Highway Worker Productivity

A construction team has three possible outcomes for the number of miles of highway built in a day: 4

Influence of Diet on Blood Pressure

A nutritionist is investigating how different dietary plans—specifically, low-carb, Mediterranean, a

Law of Large Numbers in Coin Toss Experiments

An experiment involves flipping a fair coin under different conditions. Consider two scenarios: one

Lottery Ticket Expected Outcome

A lottery ticket costs $2. The possible outcomes are: win $100 with probability 0.01, win $20 with p

Restaurant Tips: Analysis of Random Variables

In a restaurant, tips received follow this distribution: $$0$$ dollars (p = 0.1), $$5$$ dollars (p =

Sales Calls Geometric Distribution

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

Sampling Distribution of the Sample Mean from a Normal Population

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

Student Testing Strategy and Scores Analysis

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

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

University Dining Hall Food Quality Survey

A survey of university dining hall patrons was conducted to assess food quality. Out of 200 responde

Yearly Savings and Investment Return Regression Analysis

A financial analyst studies the effect of yearly savings (in thousands of dollars) on the rate of in

Biased Estimator in Quality Control

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

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 Consumption and Alertness

A study investigates whether coffee consumption is related to alertness. Two independent samples wer

Comparing Mean Reaction Times Between Two Groups

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

Dream Recall Simulation Study

A study on dream recall in college students found that the median number of dreams remembered per ni

Estimator Evaluation in Quality Control

A manufacturing process is designed to produce products weighing 500 grams. Four estimators (E1, E2,

Interpreting p-values in a Clinical Trial

In a clinical trial testing a new drug, the null hypothesis states that the drug has no effect. The

New Drug Effect on Blood Pressure Reduction

A clinical trial is evaluating a new drug that is believed to reduce blood pressure. Historically, t

Psychological Test Reliability

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

Regional Customer Satisfaction Analysis

A marketing study examines customer satisfaction in two regions. In Region A, the true satisfaction

Sample Size Calculation for Voter Support Estimation

A political survey aims to estimate the proportion of voters supporting a specific candidate with a

Sample Size Effects: Simulation Analysis

A simulation study is performed to examine the effect of sample size on the variability of the sampl

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

Social Media Use and Sleep Duration

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

Analyzing Proportions as a Function of Batch Size

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

Assessing the Fairness of a Die

A six-sided die is rolled 600 times to test for fairness. In these 600 rolls, the result "6" appears

Assessing Website Conversion Rate

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

Comparing Two Dietary Supplements

A study compares two dietary supplements. In a sample of 200 consumers for Supplement A, 140 reporte

Comparing Two Proportions: Online vs. In-Store Shopping Preferences

A researcher compares shopping preferences. In a sample of 300 online shoppers, 210 prefer online sh

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

Confidence Interval for Difference in Proportions: Homeowners vs. Renters on Energy Efficiency

A survey was conducted to compare the preference for energy efficiency improvements between homeowne

Confidence Interval for Social Media Users

A survey was conducted on 800 individuals to assess daily social media usage. Out of 800 respondents

Diet Preference in Age Groups

A study compares the proportion of individuals following a vegan diet between two age groups. Among

Educational Assessment: Confidence Interval for Passing Rate

A school administered a standardized test to 800 students, and 560 of them passed. Answer the follow

Employee Burnout Study

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

Gender Differences in Product Preference

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

Government Policy Approval Confidence Interval

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

Health Intervention Program Effectiveness

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

Hospital Safety Initiative Comparison

Two hospitals implement a safety initiative and then survey their nursing staff. In Hospital 1, 95 o

Impact of Training Program on Certification Rates

A company implemented a training program to improve certification rates among its employees. In a ra

Implications of Errors in a Safety Inspection

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

One-Sided Election Polling Analysis

In a survey of 600 likely voters, 330 support a particular candidate. The candidate’s campaign claim

Public Health Confidence Interval

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

Public Opinion on Policy Change

A survey is conducted on a new tax policy. In a simple random sample of 500 voters, 260 indicated th

Recreational Activities and Injury Rates

A health study compared injury rates for participants in contact sports versus non-contact sports. I

Social Media Influence Study

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

Social Media Usage by Gender

A survey compares social media usage among different genders. In a sample of 400 males, 320 use soci

STEM Club Gender Representation Study

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

University Enrollment Statistics

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

Vaccine Hesitancy Survey Design

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

Voter Turnout Behavior Survey

A political organization implements a get-out-the-vote campaign in several precincts and wishes to d

Web Advertisement Click-Through Rates

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

Air Conditioning Energy Consumption

A manufacturer claims that its new air conditioning unit uses on average 6.5 kilowatts of electricit

Average Household Electricity Usage

An energy study reports that for a random sample of 40 households, the average monthly electricity u

Dosage Effect on Symptom Reduction

In a clinical trial investigating the effect of a drug, researchers examine the relationship between

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 Teaching Method

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

Evaluating a Sleep Intervention

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

Evaluation of New Teaching Method Using Paired Data

An educational researcher investigates the impact of a new teaching method on student performance. A

Fuel Efficiency Analysis

A study is conducted to assess the fuel efficiency (in miles per gallon) of a new model of cars. A r

Investigating Student Reaction Times

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

Machine Calibration Paired Data

A manufacturer tests the effect of a maintenance update on machine calibration. Fifteen machines are

Paired Analysis of Blood Glucose Levels Before and After a Meal

A nutritionist is interested in the effect of a meal on blood glucose levels. Ten participants have

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

Pre- and Post-Treatment Blood Pressure

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

Pre- and Post-Treatment Blood Pressure Analysis

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

Pre-Test and Post-Test Scores Analysis

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

Quality Control: Machine Calibration

A factory employs a machine to produce metal rods. To check the machine’s calibration, two samples o

Reaction Time Hypothesis Test

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

Simulating Sampling Distribution of Daily Temperatures

A simulation study was conducted to generate the sampling distribution of the sample mean daily temp

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 in Environmental Air Quality

An environmental scientist conducts a simulation study to analyze the sampling distribution of the a

Sports Performance and Training Regimen

A sports scientist investigates the effect of two training regimens on athletic improvement. Athlete

Study Hours and GPA Analysis

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

Testing a New Drug's Effect on Cholesterol Levels

A pharmaceutical company claims that its new drug lowers LDL cholesterol levels. In a study of 12 pa

Training Hours and Employee Productivity Analysis

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

Training Program Performance Improvement

A sports coach is evaluating a new training program by measuring athletes’ performance times before

Voting Behavior and Political Affiliation

A study analyzes voting behavior among members of two political parties, Party A and Party B. The da

Yearly Comparison of Mathematics Test Scores

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

Academic Performance: Honors vs. Non-Honors

A school is investigating whether there is an association between program type (Honors vs. Non-Honor

Assessing the Fit of a Theoretical Distribution on Emergency Call Durations

Emergency call durations are categorized as Short (0–2 minutes), Medium (2–5 minutes), and Long (ove

Association between Exercise Frequency and Diet Type

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

Book Genre Popularity Study

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

Clinical Trial: Treatment Effects on Recovery Rates

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

Coffee Preference in College

Three colleges conducted surveys of 150 students each to determine their preferred type of coffee: E

Consumer Preference for Advertisement Types

A company believes that consumer preference for advertisement type follows the distribution: Online

Customer Response to Advertising: Chi-Square Test for Independence

A company’s advertising campaign is evaluated by surveying customers on their response (Positive, Ne

Customer Satisfaction Across Store Branches: Chi-Square Test for Homogeneity

A retail chain surveys customer satisfaction across three store branches. Customers are classified a

Customer Satisfaction Across Store Branches: Homogeneity Test

A retail chain with three branches (A, B, and C) surveys customer satisfaction with three response c

Customer Satisfaction Ratings Across Service Centers

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

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 Efficacy Across Regions: Homogeneity Test

A pharmaceutical company tests the effectiveness of a new drug in four regions. Each region conducts

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

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

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

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

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

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

FRQ 5: Health Supplement Side Effects

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

FRQ 12: Employee Training Program and Job Promotion

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

FRQ 15: Distribution of Wildlife Species in a National Park

Park managers expect that wildlife sightings in a national park follow a certain distribution among

FRQ 17: Customer Complaint Types and Resolution Outcomes

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

Fruit Distribution Goodness-of-Fit Test

A fruit vendor claims that the distribution of fruits in a basket follows the percentages: 40% Apple

Game Outcome Distribution

A board game produces three outcomes: win, loss, and draw. The expected probabilities for these outc

Gender and Preferred Social Media Platform

A survey of 300 teenagers gathered data on their gender (Male, Female) and their preferred social me

Gender Distribution Across College Departments

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

Independence Test: Dietary Supplements and Energy Levels

A fitness center surveyed 250 members about their use of dietary supplements (Yes/No) and their self

Job Satisfaction Among Different Occupations

A study is conducted to compare job satisfaction among four occupational groups in a school system:

Market Analysis: Brand Preference

A market analysis firm surveyed 200 consumers to determine their preference among three competing br

Political Polling: Party Affiliation and Issue Stance

A national poll cross-classifies respondents by party affiliation (Democrat, Republican, Independent

Population Distribution: Rural, Suburban, and Urban

A demographer expects that the percentages of households in a country living in Rural, Suburban, and

Race Participation in Marathon

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

Restaurant Menu Preferences

A restaurant surveys 100 customers about their preferred cuisine among four options: Italian, Chines

Student Course Preference and Major

A university surveys 300 students to determine if course delivery preference (Online vs. In-Person)

Survey Response Distribution Goodness-of-Fit Test

A survey on public opinion regarding a new policy asks respondents to choose among Agree, Neutral, a

Transportation Mode Preferences: Homogeneity Test in City vs. Suburban Areas

An urban planner surveyed residents in a city and a suburban area about their preferred transportati

Voting Methods: Chi-Square Goodness-of-Fit

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

Voting Patterns and Ballot Measure Support

A survey of 400 voters categorizes responses by party affiliation and support for a ballot measure.

Advertising Budget and Sales Revenue

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

Advertising Data: Predicting Sales

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

Advertising Impact on Sales

A retail company examines how daily advertising expenditure (in thousands of dollars) influences dai

Agricultural Study: Fertilizer and Crop Yield

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

Altitude vs Cooking Time

A culinary scientist is investigating whether altitude affects cooking time for a specific recipe. D

Blood Pressure and Sodium Intake Study

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

Coffee Consumption and Alertness

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

Consumer Spending and Income Levels

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

Effect of Class Size on Student Achievement

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

Effectiveness of a New Drug on Blood Pressure

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

Elevation and Atmospheric Pressure

Atmospheric scientists study the relationship between elevation ($$x$$, in meters) and atmospheric p

Employee Experience and Salary

A human resources study examines the relationship between years of work experience ($$x$$) and annua

Engineering: Stress and Strain in Alloys

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

Evaluating the Impact of Work Experience on Promotion Rate

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

Fuel Efficiency and Car Weight

An automotive researcher is examining the relationship between a car's weight (in pounds) and its fu

Hours of Sleep and Reaction Time

A study examines the effect of hours of sleep ($$x$$) on reaction time ($$y$$, in milliseconds) for

Impact of Fertilizer Type on Plant Growth

A researcher is studying the effect of two different fertilizers on plant growth. The amount of fert

Internet Speed and Streaming Buffer Time

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

Machine Operating Time and Defect Rate

A manufacturing plant collected data to investigate the relationship between machine operating time

Physical Activity and Weight Loss: Simulation Analysis

A researcher is studying the effect of weekly physical activity (in hours) on weight loss (in kg) us

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

Predicting Student Performance with Attendance Rates

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

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

Relationship Between Study Hours and Exam Scores

A school counselor is investigating the relationship between the number of hours a student studies a

Sports Performance: Practice Time vs Shooting Accuracy

A basketball coach investigates how weekly practice hours affect shooting accuracy percentages among

Water pH and Aquatic Life Diversity

Environmental scientists are investigating the relationship between water pH (x) and aquatic life di

Wind Speed vs Power Output

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