Stats 1.0

A professor asks students to distinguish between two broad approaches to analyzing data. One approach summarizes the information actually collected, while the other uses a sample to make conclusions about a larger group. What are these two main types of statistics?

Descriptive and inferential statistics.

A professor collects the GPAs of 200 students and creates tables, graphs, and numerical summaries showing the distribution of those GPAs without making claims about students who were not surveyed. Which type of statistics is being used?

Descriptive statistics organizes and summarizes data.

A college surveys 400 students about their study habits and uses the results to estimate the study habits of all students at the college. Which type of statistics is being used?

Inferential statistics uses data from a sample to draw conclusions about a population.

A researcher is studying the likelihood that a randomly selected student will pass a particular exam. Before collecting data, the researcher calculates the chance of different possible outcomes. What mathematical tool is the researcher using?

Probability is a mathematical tool used to study randomness and likelihood.

A fair coin is flipped once during a probability experiment. Because the coin has two equally likely outcomes, heads and tails, what is the probability of getting heads?

The probability of getting heads is 50%.

A university researcher wants to study the average amount of time spent studying by every student enrolled at the university. If the researcher defines the group of interest as every enrolled student, what does this group represent?

The population is the entire group being studied.

A researcher wants to estimate the average GPA of 20,000 college students but can only collect information from 500 students selected from that group. What does the group of 500 represent?

The sample is a smaller subset of the population.

A college has 20,000 students, and researchers randomly select 500 students to participate in a study. If the goal is to understand all 20,000 students, which group is the population?

The population is the 20,000 students.

A college has 20,000 students, and researchers randomly select 500 students for a study. Which group represents the sample?

The sample is the 500 randomly selected students.

A researcher wants to estimate the average GPA of an entire college by surveying a smaller group of students. Which characteristic would make the sample most useful for representing the college as a whole?

The sample is good when it is representative of the population.

A researcher calculates the exact average GPA of every student enrolled at a college. The resulting number describes the entire population. What is this number called?

A parameter is a number describing a population.

A researcher calculates the average GPA of 150 randomly selected students. The resulting number describes only those sampled students. What is this number called?

A statistic is a number describing a sample.

Professor Khan teaches students a memory trick to distinguish two important statistical terms: "P → P" and "S → S." A student wants to use the trick when identifying whether a numerical value describes a population or a sample. What does the memory trick mean?

Parameter = population; Statistic = sample.

A university calculates the average GPA using every student enrolled at GSU rather than selecting a smaller group. The resulting average describes the entire student population. Is this average a parameter or a statistic?

The average GPA of all students at GSU is a parameter.

Researchers randomly select 100 GSU students and calculate their average GPA to estimate the GPA of all GSU students. Is the calculated average a parameter or a statistic?

The average GPA of 100 randomly chosen GSU students is a statistic.

A researcher studies the academic performance of college students and records the GPA for each individual student. What is the variable being measured?

The variable is the GPA of each individual student.

A researcher wants to determine how much each student studies and records the number of study hours for every student in the sample. What does the variable represent?

The variable is the characteristic being measured for each individual person or thing.

A researcher records the GPAs of five students as 2.4, 3.1, 3.5, 2.8, and 4.0. What do the actual recorded numerical values represent?

The actual recorded values are data.

A college researcher records each student's GPA, and the values can be expressed numerically, such as 2.7, 3.4, and 3.9. What type of variable is GPA?

GPA is a numerical variable.

A researcher asks students which type of transportation they use to travel to campus, with possible answers including bus, car, bicycle, or walking. What type of variable is transportation type?

The transportation type is a categorical variable.

A survey asks students, "Do you own a car?" and records each response as either YES or NO. What type of variable is being measured?

The variable is categorical.

A researcher records the number of hours each student studies per week, such as 5, 8, 12, and 15 hours. What type of variable is being measured?

The variable is numerical.

A researcher asks students how they travel to school and records answers such as bus, drive, or walk. Why is this variable classified as categorical rather than numerical?

The variable is categorical because the responses represent categories rather than numerical measurements.

A college researcher wants to study spending habits among first-year students and surveys 100 randomly selected first-year students. If the goal is to generalize the findings to the entire first-year student group at the college, what is the population?

The population is all first-year students at the college.

A college researcher surveys 100 randomly selected first-year students to study their spending habits. Which group represents the sample?

The sample is the 100 randomly selected first-year students.

A researcher surveys 100 first-year students about how much they spend and wants to know the average spending amount for every first-year student at the college. Which quantity is the parameter?

The parameter is the average amount spent by all first-year students.

A researcher surveys 100 first-year students and calculates their average spending. The researcher then uses that value to estimate spending among all first-year students. Which quantity is the statistic?

The statistic is the average amount spent by the 100 students.

A researcher studying first-year students' spending records how much money each individual student spends. What is the variable in this study?

The variable is the amount of money spent by each individual first-year student.

A researcher records student spending values such as $150, $200, and $225 for students participating in a study. What do these recorded dollar amounts represent?

The recorded spending values are data.

A professional directory contains all medical doctors included in a study's target group. Researchers want to determine the proportion of these doctors who have been involved in malpractice lawsuits. What is the population?

The population is all medical doctors listed in the professional directory.

Researchers randomly select 500 doctors from a professional directory to study malpractice lawsuits. Which group represents the sample?

The sample is the 500 randomly selected doctors.

A researcher wants to determine the proportion of all doctors in a professional directory who have been involved in malpractice lawsuits. Which quantity is the parameter?

The parameter is the proportion of all doctors in the population involved in malpractice lawsuits.

Researchers calculate the proportion of the 500 randomly selected doctors who have been involved in malpractice lawsuits. They intend to use this result to estimate the proportion for the entire population. What is this calculated proportion?

The statistic is the proportion of the 500 sampled doctors involved in malpractice lawsuits.

A researcher records whether each doctor has ever been involved in a malpractice lawsuit. What is the variable being measured?

The variable is whether an individual doctor has been involved in a malpractice lawsuit.

A study records each doctor's malpractice status as YES or NO. Because the responses identify categories rather than numerical measurements, what type of variable is this?

The variable is categorical.

A researcher wants to study milk consumption among college students. The goal is to estimate the average number of glasses of milk consumed per day by every college student. What is the population?

The population is all college students.

Researchers randomly select five college students to record their daily milk consumption. What is the sample?

The sample is the five randomly selected college students.

A researcher wants the average number of glasses of milk consumed per day by all college students, not just those surveyed. Which quantity is the parameter?

The parameter is the average number of glasses drunk by all college students.

A researcher calculates the average daily milk consumption of five randomly selected college students. Which quantity is the statistic?

The statistic is the average number of glasses drunk by the five students.

A study records how many glasses of milk each individual college student drinks per day. What is the variable?

The variable is the number of glasses of milk each individual student drinks per day.

A researcher records milk consumption for five students as 0, 1, 3, 2, and 4 glasses per day. What do these recorded values represent?

The recorded values are data.

A researcher records the number of glasses of milk each student drinks per day, with values such as 0, 1, 2, and 4. What type of variable is being measured?

The variable is numerical.

A university researcher wants to estimate the average GPA of all GSU students by randomly selecting 200 students and calculating their average GPA. Which statement correctly identifies the population and sample?

All GSU students are the population and the 200 students are the sample.

A student is given four statements about parameters and statistics and must identify the correct one. Which statement is TRUE?

A parameter describes a population.

A college wants to determine the average GPA of its entire student body but surveys only students enrolled in one statistics class. What is the biggest statistical concern with using this group to represent the entire college?

The sample may not be representative.

A researcher selects a sample that closely reflects the characteristics of the population being studied. What is the most likely benefit of using this representative sample?

If a sample is representative of the population, the statistic will provide a better estimate of the population parameter.

A student is trying to remember whether a numerical result describes a population or a sample. Which memory rule from Professor Khan provides the best shortcut?

Parameter = population; Statistic = sample.