A researcher surveys 400 randomly chosen students at a university of 20,000 students to estimate how many hours per week students study. What is the population?
All 20,000 students at the university
✓
The 400 students who were surveyed
The average study time of the 400 students
The number of hours each student studies
Correct Answer
All 20,000 students at the university
The population is the entire group the researcher wants to learn about, which is every student at the university. The 400 students who were surveyed are the sample, not the population. The average study time of the 400 students is a statistic computed from the sample. The number of hours each student studies is the variable being measured.
Category: Key Terms
Question 2
In the same study, the mean weekly study time of the 400 surveyed students is an example of what?
A parameter
A statistic
✓
A population
A census
Correct Answer
A statistic
A statistic is a number that describes a sample, and the 400 students are a sample. A parameter is a number that describes the whole population, such as the true mean for all 20,000 students. A population is a group of individuals, not a number. A census would collect data from every member of the population rather than from 400 of them.
Category: Key Terms
Question 3
A pollster uses the opinions of 1,200 likely voters to draw a conclusion about all likely voters in the country. This is an example of what?
Descriptive statistics
Random assignment
Inferential statistics
✓
Nonsampling error
Correct Answer
Inferential statistics
Inferential statistics uses sample data to reach conclusions about a larger population. Descriptive statistics only organizes and summarizes the data that were collected. Random assignment is the use of chance to place subjects into treatment groups in an experiment. Nonsampling error is error from causes unrelated to sampling, such as a faulty measuring device.
Category: Key Terms
Question 4
The number of siblings a student has is what type of data?
Quantitative continuous
Qualitative nominal
Qualitative ordinal
Quantitative discrete
✓
Correct Answer
Quantitative discrete
A count of siblings is numerical and can only take whole-number values such as 0, 1 or 2, so it is quantitative discrete. Quantitative continuous data come from measuring and can take any value in a range, such as height. Qualitative nominal data are unordered categories such as eye color. Qualitative ordinal data are ordered categories such as small, medium and large.
Category: Data and Measurement
Question 5
Which of these variables is qualitative?
Blood type of a patient
✓
Number of hospital visits in a year
Body temperature in degrees Fahrenheit
Length of a hospital stay in hours
Correct Answer
Blood type of a patient
Blood type places each patient in a category such as A, B, AB or O, so it is qualitative (categorical) data. Number of hospital visits in a year is a count, which makes it quantitative discrete. Body temperature in degrees Fahrenheit is a measurement, so it is quantitative continuous. Length of a hospital stay in hours is also a measurement and is quantitative continuous.
Category: Data and Measurement
Question 6
A college sorts its students by class year (first-year, sophomore, junior, senior) and then randomly selects 10% of the students within each class year. Which sampling method is this?
Cluster sampling
Stratified sampling
✓
Systematic sampling
Convenience sampling
Correct Answer
Stratified sampling
Stratified sampling divides the population into groups that share a characteristic and then takes a random sample from every group. Cluster sampling would randomly choose some whole groups and include everyone in them. Systematic sampling selects every kth member of a list after a random start. Convenience sampling uses whoever is easiest to reach, with no random selection.
Category: Sampling Methods
Question 7
A school district randomly selects 5 of its 40 schools and surveys every teacher in those 5 schools. Which sampling method is this?
Stratified sampling
Systematic sampling
Cluster sampling
✓
Simple random sampling
Correct Answer
Cluster sampling
Cluster sampling randomly chooses some groups (here, schools) and includes every member of the chosen groups. Stratified sampling would take a random sample from inside every school. Systematic sampling would select every kth teacher from an ordered list. Simple random sampling would choose teachers individually so that every group of the same size had an equal chance.
Category: Sampling Methods
Question 8
A quality inspector picks a random starting point among the first 20 items on an assembly line and then checks every 20th item after it. Which sampling method is this?
Cluster sampling
Stratified sampling
Convenience sampling
Systematic sampling
✓
Correct Answer
Systematic sampling
Systematic sampling begins at a random point and then selects members at a fixed interval, such as every 20th item. Cluster sampling would choose whole groups of items and inspect all of them. Stratified sampling would split the items into subgroups and sample randomly from each one. Convenience sampling would inspect whichever items were easiest to grab, with no random start.
Category: Sampling Methods
Question 9
Which of these is a simple random sample of a company's employees?
Drawing 30 names at random from a list of all employees
✓
Surveying the 30 employees who are in the break room
Choosing every 10th employee on a list after a random start
Picking 10 employees at random from each of 3 departments
Correct Answer
Drawing 30 names at random from a list of all employees
Drawing 30 names at random from a complete list gives every possible group of 30 employees the same chance of selection, which defines a simple random sample. Surveying the 30 employees who are in the break room is a convenience sample. Choosing every 10th employee on a list after a random start is a systematic sample. Picking 10 employees at random from each of 3 departments is a stratified sample.
Category: Sampling Methods
Question 10
A radio station asks listeners to call in and vote on a proposed tax increase. Why are the results unlikely to represent the community?
The sample is too large to analyze
Respondents chose themselves to take part
✓
Votes are a form of quantitative data
Callers were assigned to groups at random
Correct Answer
Respondents chose themselves to take part
A call-in poll is a self-selected sample, and people who bother to call usually have stronger opinions than the community as a whole. A sample that is too large is not a problem, since larger samples are generally more reliable. Votes for or against a tax are qualitative data, not quantitative. No one was assigned at random in a call-in poll, and random assignment would not cause bias anyway.
Category: Evaluating Studies
Question 11
Two random samples of 50 students are taken from the same college, and their mean GPAs are 3.12 and 3.05. What best explains the difference between the two means?
A faulty measuring device
A lurking variable
Sampling variability
✓
Falsified data
Correct Answer
Sampling variability
Different random samples from the same population contain different individuals, so their statistics naturally differ; this is sampling variability. A faulty measuring device would cause nonsampling error and is not needed to explain the gap. A lurking variable is an extra variable that clouds a cause-and-effect conclusion in a study, which is not the issue here. Falsified data is an ethics violation, and nothing suggests it happened.
Category: Evaluating Studies
Question 12
A survey is mailed to 1,000 randomly selected homes, but only 150 are returned. Which problem does this create?
Sampling with replacement
Random assignment
The power of suggestion
Nonresponse
✓
Correct Answer
Nonresponse
When most selected people do not respond, those who do may differ from the population, so nonresponse can bias the results. Sampling with replacement means a member can be picked more than once, which has nothing to do with unreturned surveys. Random assignment places subjects into treatment groups in an experiment. The power of suggestion is the effect of a subject's expectations in an experiment.
Category: Evaluating Studies
Question 13
Daily high temperatures recorded in degrees Celsius are measured at which level?
Interval
✓
Nominal
Ordinal
Ratio
Correct Answer
Interval
Celsius temperatures are ordered and the differences between them are meaningful, but 0 degrees Celsius does not mean there is no heat, so the level is interval. Nominal data are unordered categories, and temperatures are numbers with an order. Ordinal data have an order but differences that cannot be measured, while a 10-degree difference is meaningful. Ratio data need a true zero, which the Celsius scale lacks.
Category: Data and Measurement
Question 14
A restaurant asks customers to rate their meal as poor, fair, good or excellent. At which level are these ratings measured?
Nominal
Ordinal
✓
Interval
Ratio
Correct Answer
Ordinal
The ratings have a natural order, but the distance between fair and good cannot be measured, so they are ordinal. Nominal would require categories with no order, and these ratings can be ranked. Interval would require meaningful numerical differences between values. Ratio would require numbers with a true zero.
Category: Data and Measurement
Question 15
In a sample of 40 students, 14 commute to campus by bus. What is the relative frequency of bus commuters?
0.14
0.40
0.35
✓
0.65
Correct Answer
0.35
Relative frequency is the frequency divided by the total, so 14 / 40 = 0.35. The value 0.14 comes from writing the count 14 as a decimal instead of dividing by 40. The value 0.40 comes from writing the total 40 as a decimal. The value 0.65 is the relative frequency of students who do not ride the bus, since 26 / 40 = 0.65.
Category: Frequency Tables
Question 16
A frequency table of student ages shows 6 students aged 18, 10 aged 19 and 4 aged 20, for 20 students in all. What is the cumulative relative frequency for age 19?
0.50
0.30
0.20
0.80
✓
Correct Answer
0.80
Cumulative relative frequency adds the relative frequencies up to and including a value: (6 + 10) / 20 = 16 / 20 = 0.80. The value 0.50 is the relative frequency of age 19 alone (10 / 20). The value 0.30 is the relative frequency of age 18 alone (6 / 20). The value 0.20 is the relative frequency of age 20 (4 / 20).
Category: Frequency Tables
Question 17
Patients are given 0 mg, 50 mg or 100 mg of a medication, and their blood pressure is measured after 4 weeks. What is the explanatory variable?
Dose of the medication
✓
Blood pressure after 4 weeks
The patients in the study
The 4-week time period
Correct Answer
Dose of the medication
The explanatory variable is the one the researcher controls to see its effect, which is the dose given. Blood pressure after 4 weeks is the response variable, the outcome being measured. The patients in the study are the experimental units. The 4-week time period is held the same for everyone, so it is not being varied.
Category: Experimental Design
Question 18
In an experiment testing three fertilizers on 30 tomato plants, each individual plant is what?
A treatment
An experimental unit
✓
A response variable
A lurking variable
Correct Answer
An experimental unit
An experimental unit is a single individual or object that receives a treatment and is measured, here one plant. A treatment is one of the fertilizers being compared. A response variable is the outcome measured, such as plant height or tomato yield. A lurking variable is an extra variable, such as sunlight, that could affect the response.
Category: Experimental Design
Question 19
Why do researchers randomly assign subjects to treatment groups in an experiment?
To guarantee the sample matches the population
To keep subjects unaware of their own treatment
To spread lurking variables evenly across groups
✓
To increase the number of subjects in the study
Correct Answer
To spread lurking variables evenly across groups
Random assignment makes the groups similar on average, so lurking variables such as age or diet are spread roughly equally and differences in the response can be credited to the treatment. To guarantee the sample matches the population is not possible, and making a sample representative is the job of random sampling rather than random assignment. To keep subjects unaware of their own treatment is the purpose of blinding. To increase the number of subjects in the study requires recruiting more people, which assignment does not do.
Category: Experimental Design
Question 20
In a drug trial, neither the patients nor the doctors who evaluate them know which patients received the real drug. What is this design called?
Single-blind
Unblinded
Observational
Double-blind
✓
Correct Answer
Double-blind
A double-blind design keeps both the subjects and the researchers who interact with them unaware of who gets the active treatment. Single-blind keeps only one party, usually the subjects, unaware. Unblinded means everyone knows who receives which treatment. Observational describes a study that imposes no treatment at all, while this trial assigns a drug.
Category: Experimental Design