AP Statistics FRQ Room

Almond Packet Weight Confidence Interval

A quality control team at an almond packaging company wants to estimate the mean weight of its packe

Application of the Empirical Rule to IQ Scores

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

Basketball Free Throw Percentage Confidence Interval

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

Blood Pressure Analysis in Clinical Trial

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

Calculating Variance and Standard Deviation for Book Counts

The numbers of books read by 10 students in a month are recorded as: {3, 4, 2, 5, 6, 4, 3, 3, 4, 5}.

Charitable Donation Timing by Age Group

A charity collected data on donation timings (Morning, Afternoon, Evening) and donor age group (Youn

Daily Step Count Hypothesis Test

A fitness app collects data from a random sample of 40 users. The sample shows an average daily step

Data Entry Error and its Impact on Summary Statistics

A delivery company recorded the number of deliveries in a day. The correct data set is: {50, 55, 60,

Effect of a Multiplicative Transformation on Distance Data

A group of athletes has their running distances (in kilometers) recorded as: {5, 6, 8, 7, 10, 9}. Th

Effect of Constant Adjustments on Mean Salary

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

Effectiveness of a New Drug

A clinical trial is conducted to evaluate the effectiveness of a new drug in improving patient outco

Effects of Adding a Constant on Measures of Spread

Consider the dataset of exam scores: {65, 70, 75, 80, 85}. Answer the following:

Effects of Linear Transformation on Data

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

Employee Salary Adjustments

A company’s six employee salaries (in dollars) are as follows: {3000, 7000, 15000, 22000, 23000, 380

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

Lottery Ticket Analysis

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

Marketing Campaign Reach by Region

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

Online Shopping Preference by Age Group

An online survey collected responses about shopping behavior by categorizing respondents into age gr

Opinions on School Start Times

Two high schools surveyed their students to determine whether they favor a later school start time.

Parent Survey on School Length

A survey of 2000 parents asked which school year length they preferred. The following table summariz

Residual Analysis: Car Efficiency versus Engine Size

A study investigates the relationship between engine size (in liters) and fuel efficiency (in miles

Restaurant Preference and Time Slot

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

Simulated Sampling Distribution of the Standard Deviation

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

Simulation and Transformation Effects on the Sampling Distribution

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

Social Media Usage and Employee Productivity

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

Stock Price Trends Through Parallel Boxplots

A series of parallel boxplots shows the daily price fluctuations of a particular stock over a 5-year

Student Major and Internship Status

A study of 200 college students recorded their major (STEM or Non-STEM) and internship status (Had I

Advertising Campaign and Sales Analysis

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

Advertising Spend and Sales Revenue

A company collected monthly data over one year on its advertising expenditure (in thousands of dolla

Analysis of Marketing Campaign Data: Sales vs. Advertisements

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

Analyzing Curvilinear Relationship and Data Transformation

A botanist records the amount of fertilizer applied (x, in grams) and the resulting plant growth (y,

App Usage Trend: Free vs Premium Users

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

Call Duration Analysis in a Service Center

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

Coffee Shop Sales Analysis

A local coffee shop has recorded data on daily advertising expenditure (in dollars) and the correspo

Comparing Two Regression Models for Chlorophyll Content Prediction

A biologist is studying the relationship between light intensity (x) and chlorophyll content in leav

Constructing a Scatterplot from Given Data

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

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

Email Marketing Response Rates

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

Employee Training Effectiveness

A company evaluated the effectiveness of two training methods by measuring subsequent job performanc

Geometric Distribution of Quick Transactions at a Bank

At a bank teller, the probability that a customer completes a transaction in less than 5 minutes is

Health Study on Diet and Activity

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

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

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

Impact of Study Environment on Academic Achievement

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

Nonparametric Alternatives to Linear Regression

Sometimes the assumptions of linear regression (such as linearity and homoscedasticity) are violated

Pets and Stress Levels

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

Regression Analysis of Movie Attendance and Concession Sales

A movie theater records daily attendance (x) and the number of concession sales (y, measured in hund

Residual Analysis in House Price Prediction

A real estate analyst develops a linear regression model to predict house prices (in $1000s) from ho

Simulation Study for Confidence Intervals in Linear Regression Predictions

A marketing analyst uses simulation to assess the performance of confidence intervals in predicting

Study Habits and Exam Pass Rates

A researcher compared exam pass rates between two groups of students enrolled in different study pro

Study Techniques and Exam Performance

A researcher collected data on the number of hours college students spent using active study techniq

Using Residual Plots to Assess Fit in Advertising and Sales Data

A company collects data on its weekly advertising budget (in $1000s, x) and weekly sales revenue (in

Wait Time and Meal Satisfaction

A restaurant collected data from 40 customers on their wait time (in minutes) and meal satisfaction

Agricultural Practices and Crop Yields

Farmers are considering an innovative agricultural practice that may increase crop yields. An observ

Analysis of Recycling Behavior

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

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

Assessing Nonresponse Bias in Telephone Surveys

During a telephone survey on community health, only 40% of the contacted individuals respond. Answer

Assessing Systematic Sampling in a Household Survey

A market research firm wants to survey household expenditures and decides to use systematic sampling

Assessing the Impact of Sampling Bias through Simulation

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

Clinical Trial on Weight Loss Programs

A randomized controlled trial compares two weight loss programs. Program A (n = 40) results in an av

Comparing Stratified and Cluster Sampling Methods in a Health Survey

A public health researcher is designing a survey to assess attitudes toward vaccination in a multi-n

Designing a Double-Blind Experiment for a New Drug

A pharmaceutical company intends to test a new drug aimed at reducing blood pressure. To eliminate b

Designing a Stratified Random Sample for Student Opinions on Distance Learning

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

Diet, Weight Loss, and Regression Analysis

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

Evaluating a Matched Pairs Design in a Weight Loss Study

Researchers compare two diets by having each participant follow both diets for a specified period, w

Evaluating Survey Question Wording Bias

Two versions of a survey question on school lunch satisfaction have been designed. Version A states:

Evaluating the Sampling Frame in an Urban Survey

A research team plans to survey residents of a large urban area on community services. They initiall

Hypergeometric Distribution in Quality Inspection

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

Influence of Outliers on the Sampling Distribution of the Sample Median

In studies of household incomes, extreme high incomes (outliers) can heavily influence the sample me

Online Tutoring and Student Performance

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

Quality Control in Manufacturing

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

Random Assignment in a Placebo-Controlled Medical Trial

A medical researcher plans a clinical trial to test the effectiveness of a new drug for migraine rel

Regression Analysis: Estimating Crop Yield Based on Rainfall

An agricultural scientist examines the effect of annual rainfall on the yield of a specific crop. Ba

Remote Learning Effectiveness

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

Scatterplot Analysis and Regression Line Interpretation

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

Systematic Sampling in a Voter Preference Survey

A polling organization is using systematic sampling to select registered voters from a telephone dir

Traffic Flow Analysis

A transportation department uses systematic sampling to count the number of vehicles passing a check

Ad Spend and Market Share Regression Analysis

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

Basic Probability Rules with Test Strategies

A literacy test was administered to 830 participants. The table below summarizes the number of parti

Bootstrap Sampling Distribution of the Sample Mean

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

Carnival Game of Chance: Payoff Transformations

A carnival game offers different monetary payoffs with the following probabilities: | Payoff ($$\$\

Charity Lottery Expected Outcome

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

Charity Lottery Expected Value Analysis

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

Coin Toss Experiment and Sample Size Effects

Consider an experiment where a fair coin is tossed repeatedly. Answer the following:

Comparing Simulation Results for Rainy Days

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

Cumulative Probability Distribution in AP Exam Scores

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

Customer Satisfaction Survey on New Service Protocol

A company is testing a new customer service protocol to improve satisfaction. Customers are randomly

Error Rates in Manufacturing by Shift

A manufacturing plant recorded error types during different shifts. The data is summarized below: |

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

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

Highway Construction: Expected Daily Miles

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

Investigative Study on Public Health Intervention

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

Law of Large Numbers in Coin Toss Games

Consider a game where a player repeatedly flips a fair coin. The game has two winning conditions: In

Library Book Borrowing Times

A public library claims that the average time a book is borrowed is 3 weeks. A random sample of 40 b

Restaurant Order Times

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

Sampling Distribution of the Interquartile Range (IQR) via Simulation

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

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

Small Business Daily Revenue Analysis

A small business tracked its daily revenue over a period of 30 days. The sample mean daily revenue w

Store Customer Satisfaction Survey

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

Student Majors and Graduation Outcome

A university tracked graduation outcomes for 300 students by major. The summarized data is provided

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

Urban Traffic Volume and Air Quality

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

Weather Impact on Road Conditions

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

Applicability of the Central Limit Theorem for Skewed Data

Consider a population with a heavily right-skewed distribution having a mean of $$\mu=50$$ and a sta

Blood Pressure Reduction Study

A study examines whether a dietary supplement affects blood pressure. In the supplement group, the a

Bootstrapping and the Sampling Distribution of the Mean

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

Central Limit Theorem in Quality Control

A flour packaging machine fills bags that are intended to weigh 50 pounds on average with a standard

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

Comparing Mean Reaction Times Between Two Groups

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

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

Comparing Variability in Two Measurement Methods

Two independent methods are used to measure the voltage of a battery. Method 1 produces individual m

Consumer Reviews: Variability Analysis

A popular online product has consumer ratings on a 1-to-5 star scale. In a random sample of 100 revi

Diet Preferences and Exercise Habits

A health survey sought to determine if there is any association between an individual’s diet prefere

Difference in Proportions: Fast Food Restaurant Study

A study compares customer behavior at two fast-food restaurants. At the revamped restaurant, $$25\%$

Effect of Sample Size on Variability

In a manufacturing process, the diameters of bearings are measured. Individual measurements have a s

Election Polling Proportions

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

Evaluating Biased and Unbiased Estimators

A quality control manager is evaluating five different estimators (labeled A through E) for estimati

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

Genetic Mutations in New Fathers

It is estimated that 40-year-old men contribute on average $$65$$ genetic mutations to their offspri

Lightbulb Life Expectancy Analysis

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

Manufacturing Process Consistency and Variability

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

Math Anxiety Brain Activity Proportions

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

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 Means: Academic Test Scores

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

Sampling Distribution for Differences in Sample Proportions in Political Polling

In a political poll, two districts are surveyed. In District A, 60% of 500 voters support a policy,

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 of the Maximum: Weather Temperature Extremes

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

Simulating the Sampling Distribution of the Range

A researcher is interested in the range of scores on a standardized test. The population range is kn

Survey on Learning App Preference

In a high school, it is believed that $$65\%$$ of students prefer using a new learning app. A random

Analysis of Survey Data on Online Learning

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

Analyzing Voter Turnout Using Confidence Intervals

An exit poll of 800 voters revealed that 560 voted in favor of Candidate Y. Construct a 95% confiden

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

Business Model Customer Return Rate Comparison

A company compares two business models by examining customer return rates. For Model A, 312 out of 5

Coffee Preference by Age Groups

A coffee shop surveyed customers on their coffee preference, classifying them as either preferring B

Comparing Test Pass Rates

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

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

Confidence Interval for a Population Proportion

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

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

Customer Satisfaction Survey by Region

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

Effectiveness of a New Marketing Strategy

A company implemented a new marketing strategy aimed at increasing customer conversion rates during

Effectiveness of a Social Media Campaign

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

Employee Retention in a Tech Firm

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

Healthy Meals Experiment Design

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

Interpreting a Confidence Interval for Hybrid Learning Preference

At a high school, a survey of 100 students reveals that 40 prefer a hybrid learning model.

Marketing Survey: Brand Loyalty Across Regions

A marketing survey compares brand loyalty across two regions. In Region 1, 210 out of 300 respondent

Nutrition Labeling Impact Study

A government agency implements a policy requiring prominent nutritional labels on packaged foods. A

Political Polling: Candidate Approval

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

Sample Size and Margin of Error Trade-Off Analysis

A political analyst is planning a poll and is considering two sample sizes. One sample of 300 respon

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

Significance Testing of Proportion Differences in Crime Rates

In a survey, 55 out of 200 residents in City A and 40 out of 250 residents in City B reported feelin

Social Media Influence Study

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

Social Media Usage Among Age Groups

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

Sports Participation by Gender and Sport Type

A survey collected data on sports participation, recording the favorite sport type as either 'Team S

Student Opinion on School Lunch Quality

A survey of 250 students at a high school found that 180 students reported that the school lunches a

Testing for a Rare Event Proportion

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

Type I and Type II Errors in a Drug Trial

In a clinical trial of a new drug, the null hypothesis states that the drug's side effect rate is 10

Voter Turnout Behavior Survey

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

BMI and Systolic Blood Pressure Analysis

The scatterplot below shows data on body mass index (BMI, x-axis) and systolic blood pressure in mmH

Career Development Program

A corporation has implemented a career development program and wishes to assess its impact on employ

Comparing Manufacturing Processes

A company uses two different processes to manufacture a particular part. Process X is evaluated on a

Comparing Recovery Times in Two Hospitals

A study compares patient recovery times (in days) following a standard surgical procedure at two dif

Comparing Two Diets

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

Customer Wait Time in Service

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

Diet Choice and Energy Levels

A nutritionist investigates whether there is an association between diet type (Vegetarian vs. Omnivo

Employee Training and Productivity Outcome

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

Employee Training Effectiveness

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

Exam Score Analysis with Unequal Sample Sizes

A researcher compares exam scores between two sections of a course. Section A (n = 18) has a mean sc

Impact of Training Programs on Test Scores

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

Income Analysis for a Tech Company

A tech company wants to estimate the average annual bonus received by its employees. A survey of 22

Investigative Analysis of Customer Service Performance Metrics

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

Light Bulb Lifespan Hypothesis Test

A company advertises that its light bulbs have an average lifespan of 1200 hours. A quality control

Manufacturing Measurement Variability

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

New Coffee Blend and Alertness Test

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

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

Quality Control in Food Packaging

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

Randomized Field Experiment on Stress Reduction

A research team is interested in determining whether a mindfulness training program reduces stress l

Reaction Time One-Sample t-Test

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

SAT Preparation Class Improvement

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

Simulating Sampling Distribution of Chip Weight

A chip manufacturing factory is investigating the average weight of its chips. A simulation was perf

Simulation of Sampling Distribution for Mean Crop Yield

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

Simulation of Sampling Distribution for Mean Recovery Time

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

Simulation of Sampling Distribution in a Clinical Trial

A medical researcher conducts a simulation to analyze the sampling distribution of the mean systolic

Simulation of Sampling Distribution in Environmental Air Quality

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

Simulation of Sampling Distribution of Mean Reaction Times

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

Sports Performance and Training Regimen

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

Temperature and Ice Cream Sales Analysis

The scatterplot below shows data on daily temperature in °F (x-axis) and the number of ice cream con

Test Score Improvement Analysis in a Preparation Class

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

Weight Reduction Program Evaluation

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

Workplace Wellness Program Evaluation

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

Advertising Channels Effectiveness: Homogeneity Test

A company wants to determine if the effectiveness of three advertising channels (TV, Online, Print)

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

Clinical Trial: Treatment Effects on Recovery Rates

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

Diet and Exercise Frequency: Independence Test

A health study of 240 participants recorded data on diet quality (Healthy, Unhealthy) and exercise f

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

Effect of Marketing Campaign on Brand Awareness

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

Employee Training Program: Comparing Certifications Across Departments

A company is evaluating the effectiveness of a new training program by comparing certification rates

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,

Genetic Trait Distribution Goodness-of-Fit

In a genetic cross the expected phenotypic ratio for a trait is 3:1 (dominant: recessive). A botanis

Genotype Ratios: Goodness-of-Fit Test in a Biology Experiment

In a genetic cross, the expected Mendelian ratio for three genotypes is $$1:2:1$$. In a sample of 16

Goodness-of-Fit for Beverage Preferences

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

Goodness-of-Fit Test in Marketing Campaign Response

A company’s marketing campaign is expected to yield customer reactions in five groups with the follo

Homogeneity in Dietary Habits Across Regions

Nutrition researchers surveyed individuals from three regions regarding their dietary habits: Omnivo

Independence Test: Voting Preference and Gender

A survey of 500 voters collected data on voting preference (Candidate A, Candidate B, Other) and gen

Market Research: Chi-Square Test for Homogeneity of Brand Choices

A market researcher wishes to determine whether consumer brand preference is consistent across three

Participation in Extracurricular Activities: Chi-Square Test for Homogeneity

A school district wants to compare participation rates in extracurricular activities among high scho

Population Distribution: Rural, Suburban, and Urban

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

Product Defect Rates – Chi-Square Goodness-of-Fit

A quality control engineer hypothesizes that defects in a product occur with equal probability among

Public Transportation and Demographics: Chi-Square Test for Independence

City planners conducted a survey of 300 residents to determine if the preferred mode of transportati

Smartphone Brand Preference

A market research firm expects that smartphone brand preferences will follow the proportions: Brand

Social Media Platform Usage

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

Social Media Platform Usage and Age: Test for Independence

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

Species Distribution in a Wildlife Reserve

In a wildlife reserve, the theoretical model predicts that the species distribution should be: Mamma

Sporting Event Results: Homogeneity Test

A study investigates whether the win distribution among five tournament teams differs. Each team's r

Survey on Preferred Modes of Transportation

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

Test for Independence: Music Preference and Age Group

A survey of 300 individuals recorded their favorite music genre (Rock, Pop, Classical) and age group

Coffee Consumption and Alertness

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

Comparing Slopes for Tutoring Effects on Test Score Improvement

A school district evaluates the effect of after-school tutoring on test score improvement for studen

Consumer Spending and Income Levels

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

Crop Yields and Fertilizer Usage

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

Daily Steps vs Calorie Burn

A fitness app developer examined the relationship between the number of daily steps and calorie burn

Daily Study Hours and GPA

Researchers are interested in analyzing the relationship between the number of hours students study

Education Research: Impact of Class Size on Performance Simulation

An education researcher is investigating the impact of class size on average student test scores. A

Employee Performance and Training Hours

A company is assessing employee performance scores (out of 100) based on the number of training hour

Employee Salary and Years of Experience

A human resources analyst uses years of experience (x) to predict annual salary in thousands of doll

Energy Consumption and Outdoor Temperature

A study on 30 households examined the relationship between outdoor temperature (x, in °F) and energy

Energy Consumption and Temperature: Simulation Study

A data analyst is investigating the relationship between ambient temperature (in $$^\circ C$$) and h

Engine Size and Emissions

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

Hours of Training and Athletic Performance

A sports scientist examines the relationship between hours of training per week ($$x$$) and athletic

Housing Price Estimation

A real estate analyst examines the relationship between the age of a house (in years) and its price

Influence of Advertising Budget on Sales

A firm is investigating the effect of its advertising budget (in thousands of dollars) on weekly sal

Manufacturing Defects and Operation Time

In a manufacturing process, data was collected to analyze the relationship between machine operation

Manufacturing Quality Control

A quality control engineer investigates the relationship between machine operation time (in hours) a

Marketing Campaign Effectiveness Simulation

A marketing analyst is examining the relationship between advertising spending (in dollars) and sale

Medical Dosage and Blood Pressure Response

A clinical trial tests the impact of a new medication dosage ($$x$$, in mg) on blood pressure reduct

Medication Dosage and Blood Pressure Reduction

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

Practice Time and Music Performance Skill

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

Rainfall and Crop Yield

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

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 Reaction Time

A psychology experiment studies the effect of sleep duration (in hours) on reaction time (in millise

Social Media Use and Academic Performance

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

Student Performance and Attendance

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

Tree Growth Analysis: Simulated Slope Distribution

An ecologist is studying the relationship between the age of trees and their heights. The ecologist

Urban vs Rural Pollution Levels

An environmental study examined the relationship between daily traffic volume (in thousands of vehic

Weather Forecasting: Humidity vs. Chance of Precipitation

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

Years of Experience and Salary Increase

A study investigated the relationship between years of job experience (x) and annual salary (in thou