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WorksheetsStatistical Methods
Total questions: 150
Worksheet time: 1hrs 15mins
The higher the temperature of the air in the oven, the faster a cake will bake. Find the explanatory variable.
Oven temperature
Time to bake
Lemon trees receiving the most water produced the most lemons. Find the explanatory variable.
Water received
Lemons produced
The time it takes to run depends on the person's running speed. Find the response variables.
Time
Running speed
A study was done to find if different tire treads affect the braking distance of a car. Explanatory variables.
Braking distance
Tire treads
The higher the temperature of the air in the oven, the faster a cake will bake. Find the response variable.
Oven temperature
Time to bake
An explanatory variable is...
Dependent
Independent
A response variable is...
Depedent
Independent
An explanatory variable is on the Y axis.
True
False
The response variable can be found along the Y axis.
True
False
The explanatory variable is the variable that we expect to explain or predict the response variable.
True
False
The response variable is the outcome or result of the study.
True
False
We wish to investigate the relationship between the number seeds planted in a garden and the number of fruit grown. The explanatory variable (EV) is
The number of fruit grown
The amount of soil in the garden
The number of hours spent watering the plants
The number of seeds planted
None of the above
We wish to investigate the relationship between the time spent shopping and the number of items bought. The response variable (RV) is
The number of items bought
The number of items at the shop
The time spent shopping
The time spent getting to the shops
None of the above
What is the explanatory variable in a study?
The variable that measures the outcome of the study
The variable that explains the outcome of the study
The variable plotted on the x-axis of a scatter plot
The variable plotted on the y-axis of a scatter plot
The amount of time studying for your next test and the grade you earn on it. Which is the explanatory variable?
Amount of time studying for your next test
Grade you earn
The amount of time studying for your next test and the grade you earn on it. Which is the response variable?
Amount of time studying for your next test
Grade you earn
Records of sales of umbrellas and amount of rainfall suggests that there is a strong positive relationship between the two variables. What do you think about the situation in terms of explanatory and response variables?
Amount of sales of umbrellas is an explanatory variable.
Amount of rainfall is an explanatory variable
The connection between the variables is not clear
The two variables are independent of each other.
In the relationship between the number seeds planted in a garden and the number of fruit grown. The response variable is
The number of fruit grown
The amount of soil in the garden
The number of hours spent watering the plants
The number of seeds planted
Which of the following is true?
We use the response variable to explain changes that might be observed in the explanatory variable.
The explanatory variable is the variable we expect to be explained by the response variable
The response variable is also known as the predictor variable
The explanatory variable is used to explain or predict the value of the response variable
In a survey at school, it is found that grades in Mathematics and hours of time spent on completing homework has an association. Which variable is the response variable?
Connection between the variables is not clear
Time spent completing homework
Grade in mathematics
Time spent completing homework as it determines the grade in mathematics.
Households consume much more electricity when the weather is warmer. What is the explanatory variable?
Temperature
Electricity
Households consume much more electricity when the weather is warmer. What is the response variable?
Temperature
Electricity
The response variable is:
The variable we expect to explain or predict the value of the explanatory variable.
Sometimes called the independent variable (IV)
The variable we expect to change in response to the explanatory variable
Also known as EV
We wish to investigate whether a person’s age can be predicted from their IQ score. Which is the explanatory variable (EV)?
Age
IQ Score
Both Age and IQ Score
None of the Above
Studies have shown that the grades earned by a student depend on the amount of hours spent studying. Which is the response variable (RV)?
Hours spent studying
Grades earned
Both Grades earned and Hours spent studying
None of the above
An admissions officer at Columbia University believes that the math SAT score for incoming students can be predicted using their reading and writing SAT score. The scatterplot shows the reading and writing scores and math SAT scores of 15 incoming students at Columbia University. Which variable is the explanatory variable? Which is the response variable?
Reading and writing SAT score is the explanatory variable; math SAT score is the response variable.
Math SAT score is the explanatory variable; reading and writing SAT score is the response variable.
Both are explanatory variables.
Both are response variables.
In a study of the age of students and whether they are allowed to stay up past 9pm on a school night, which is the explanatory variable?
Whether the student can stay up past 9pm on a school night
The age of the student
Not enough information
9pm? I'm in bed by 7! LOL :)
In a study of the age of students and whether they are allowed to stay up past 9pm on a school night, which is the response variable?
Whether or not a student is allowed to stay up past 9pm on a school night
The age of the student.
Not enough information.
9pm? I'm in bed by 7! LOL :)
Identify the explanatory variable:
Residential status (on- vs off-campus) and year in college
Residential Status
Year in College
Identify the response variable:
Whether or not a person develops lung cancer and smoking status (smoker or non-smoker).
Whether or not a person develops lung cancer.
Smoking status (smoker or non-smoker)
Mrs. S knew that students who attended her morning study sessions performed better on math tests but very few students attended them. She wanted to test if bringing doughnuts to the study sessions would increase student attendance. She continued to advertise the sessions in the same method and hold sessions at the same time. The only difference was that she brought doughnuts to the session. She had a 50% increase in attendance when she brought the doughnuts.
What is the dependent (response) variable?
The test
The doughnuts
The number of students who attend the study session
The study session
Mrs. S knew that students who attended her morning study sessions performed better on math tests but very few students attended them. She wanted to test if bringing doughnuts to the study sessions would increase student attendance. She continued to advertise the sessions in the same method and hold sessions at the same time. The only difference was that she brought doughnuts to the session. She had a 50% increase in attendance when she brought the doughnuts.
What is the independent (explanatory) variable?
The test
The doughnuts
The study session
The number of students in attendance
Interview every 10th student who enters the school in the morning.
simple random
voluntary response
systematic
convenience
Assign each car in a dealership a number and then use a random-number table to select the cars to be inspected.
systematic
simple random sample
convenience
Self - selected (volunteer)
Political webpages often allow readers to rate (if they want to) whether they strongly agree, agree, disagree, or strongly disagree with the President's decision on any given situation. This is a form of:
Volunteer Response
Convenience Sampling
Simple Random Sampling
Systematic Random Sampling
Marianne wanted to know students' opinion on the new schedule at school. She survey's the first 30 students who come into her class.
Convenience Sampling
Systematic Random Sampling
Simple Random Sampling
Volunteer response
A teacher wants to know the average time spent doing homework by the students in her class of 20 girls and 5 boys.
She picks the student in every 5th seat.
Simple Random
Systematic
voluntary response
convenience
A teacher wants to know the average time spent doing homework by the students in her class of 20 girls and 5 boys.
She selects the five closest to her desk.
simple random
Self Selected.
Convenience
Systematic Random
A teacher wants to know the average time spent doing homework by the students in her class of 20 girls and 5 boys.
She selects the first five who raise their hands.
Systematic
Convenience
Volunteer Response
Simple Random
This is a form of:
Elise, a supermarket employee, approached 50 random customers and asked whether they would be willing to discuss what they like most about the store. She interviewed the 22 who said yes. Is this sample of the supermarket's customers likely to be biased?
yes
no
What time did the students in class wake up this morning?
STATISTICAL
NON
STATISTICAL
What were the high temperatures in each city in Connecticut yesterday?
STATISTICAL
NON
STATISTICAL
How tall is the tallest person in class?
STATISTICAL
NON
STATISTICAL
What is the difference between the scores on your last two spelling tests?
STATISTICAL
NON
STATISTICAL
How many hours of screen time does each student in class have per day?
STATISTICAL
NON
STATISTICAL
How many siblings does your teacher have?
STATISTICAL
NON
STATISTICAL
How many siblings does your each student in class have?
STATISTICAL
NON
STATISTICAL
How many different states has the principal visited?
STATISTICAL
NON
STATISTICAL
How many books have each of my friends read this year?
STATISTICAL
NON
STATISTICAL
How old is your teacher?
STATISTICAL
NON
STATISTICAL
How many free throws did each player on the team miss in today's game?
STATISTICAL
NON
STATISTICAL
How many pets does each student in class own?
STATISTICAL
NON
STATISTICAL
How much time did you spend listening to music each day this week?
STATISTICAL
NON
STATISTICAL
How much time per day do you spend listening to music?
STATISTICAL
NON
STATISTICAL
What is the color of your cat?
STATISTICAL
NON
STATISTICAL
How many pepperonis are on each pizza?
STATISTICAL
NON
STATISTICAL
How many marshmallows can each student fit in their mouth?
STATISTICAL
NON
STATISTICAL
How many apps do students have on their phones?
STATISTICAL
NON
STATISTICAL
What are the heights of the players on the Spartans football team?
STATISTICAL
NON
STATISTICAL
How old were you when you first learned to ride a bicycle?
STATISTICAL
NON
STATISTICAL
What is the difference between a sample and a population?
Populations only consider a portion of the sample being studied.
Samples only consider a portion of the population being studied.
Populations do not always represent the entire group of people in question.
Samples are generally much larger than populations.
Mrs. Delgado asks the first ten students at Clinton Elementary about what they think the new school's mascot should be. Identify the population and sample.
Population: First ten students
Sample: All students at Clinton Elementary
Population: All students at Clinton Elementary
Sample: First ten students
A school principal wants to offer an after-school club setting. She decided to survey 300 students about this. Which word best describes the group of 300 students?
Population
Sample
Census
Prediction
A survey of 976 American households found that 32% of the households own two cars. Identify the the sample. {hint: a survey of what __)
All American households
976 American households
32% of Americans own two cars
two cars
80 7th graders at CMS were asked what their favorite season was. Does this represent a population or a sample?
sample
Population
If a population consists of 500 people and a sample of 50 people is taken, what is the sample size as a percentage of the population?
10%
20%
5%
50%
A (a) is an entire group, while a (b) is a smaller chosen part.
population
sample
80 7th graders at CMS were asked what their favorite season was. Does this represent a population or a sample?
sample
Population
30% out of 200 Mr. Tran’s students earned A for the final grade average from the last semester.
Identify the sample {a partial part of the large group}
200 Forest Park students
30% of Forest Park students
200 Mr. Tran's students
30% of 200 Mr. Tran's students
Identify the population {which group was mentioned in the statement }
200 Forest Park students
30% of Forest Park students
200 Mr. Tran's students
30% of 200 Mr. Tran's students
True or False: all samples lead to a good prediction about an entire population.
True
False
What is a smaller, representative group drawn from a population?
unit
sample
parameter
statistic
The entire set of items (who or what) from which data can be selected
survey
parameter
population
sample
Population or Sample?
A survey of 1353 American households found that 18% of the households own a computer.
Population
Sample
Population or Sample?
The average weight of every person entering the mall within 3 hour period was 146 lb.
Population
Sample
Population or Sample?
All of the teachers in a school are surveyed on their meeting time preferences.
Population
Sample
Identify the population and parameter:
To determine the food preferences of their customers, the owners of a restaurant randomly choose 20 customers on Friday to participate in a survey.
population: the 20 randomly chosen customers surveyed
parameter: food preferences for the 20 randomly chosen customers
population: all customers of the restaurant
parameter: food preferences for all of the restaurant's customers
population: all people in the nation
parameter: food preferences for the 20 randomly chosen customers
none of these
A survey of 500 spectators from a stadium with 42,000 spectators.
Population
Sample
The annual salary of each pharmacist at a pharmacy.
Population
Sample
The cholesterol levels of 20 patients in a hospital with 100 patients.
Population
Sample
One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared.
Observational Study
Experiment
You look at data to see if students who have a 4.0 grade point average study more than those who do not.
experiment
observational study
You compare the health of students who walk to school to the health of students who ride the bus
experiment
observational study
A researcher randomly assigned boys and girls to each of two groups. One group was assigned to watch a violent television program while the other group watched a nonviolent program. The children's behavior was then recorded for incidences of aggressive behavior. This research method is best characterized as...
experimental
Observation
A psychologist designed a study to test the effects of cell phone use on driving safety. Participants were randomly assigned either to drive an automobile simulator while talking to a friend on a cell phone or to drive a simulator without talking on a phone.
Which type of research does the scenario describe?
Experiment
Observation
To test the effects of breakfast on grades I ask my students if they ate breakfast and then compare the breakfast eaters grades to the non-breakfast eaters.
This is an example of:
Observational study
Experiment
Rats with cancer are divided into two groups. One group receives 5 milligrams of a medication that is thought to fight cancer and the other receives 10 mg. After 2 years, the spread of cancer is measured.
Observational Study
Experiment
treatment is imposed upon a subject and a response is recorded
observational study
experiment
treatment
unmedicated treatment made to look like the real treatment
control
experimental
placebo
An (a) does not have treatments imposed.
An (b) has treatments imposed.
Cause and effect (causation) can only be proven with EXPERIMENTS.
True
False
350 athletes who had suffered hamstring injuries were randomly assigned to one of two different exercise programs. The first group is assigned to a static stretching program and the second group is assigned to an agility and trunk stabilization program. The researchers recorded how long it took the athletes to return to sports. What is the Sample?
Duration of the return
Two different exercise programs
350 athletes
350 athletes who had suffered hamstring injuries were randomly assigned to one of two different exercise programs. The first group is assigned to a static stretching program and the second group is assigned to an agility and trunk stabilization program. The researchers recorded how long it took the athletes to return to sports. What are the treatments?
Duration of the return
Two different exercise programs
350 athletes
350 athletes who had suffered hamstring injuries were randomly assigned to one of two different exercise programs. The first group is assigned to a static stretching program and the second group is assigned to an agility and trunk stabilization program. The researchers recorded how long it took the athletes to return to sports. What is the response?
Duration of the return
Two different exercise programs
350 athletes
A marketing firm conducts a study where 200 people are shown either a 30 second animated commercial or a 30 second live action commercial for the same product. After viewing the commercial, subjects are asked to rate the product ‘1’ to ’10.’ What is the Sample in this experiment.
200 people
Animated and Live action commercials
Rating the product
A marketing firm conducts a study where 200 people are shown either a 30 second animated commercial or a 30 second live action commercial for the same product. After viewing the commercial, subjects are asked to rate the product ‘1’ to ’10.’ What is the RESPONSE in this experiment.
200 people
Animated and Live action commercials
Rating the product
A marketing firm conducts a study where 200 people are shown either a 30 second animated commercial or a 30 second live action commercial for the same product. After viewing the commercial, subjects are asked to rate the product ‘1’ to ’10.’ What are the TREATMENTS in this experiment.
200 people
Animated and Live action commercials
Rating the product
One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared. What is the response variable?
herbal supplement/placebo
number of illnesses
One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared. What is the explanatory variable?
herbal supplement/placebo
number of illnesses
An entire set of items from which data can be selected
sample
population
survey
observational study
Occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.
confounding
response
explanatory
A survey of 976 American households found that 32% of the households own two cars. Identify the the sample. {hint: a survey of what __)
All American households
976 American households
32% of Americans own two cars
two cars
A survey of 976 American households found that 32% of the households own two cars. Identify the the population. {hint: which group was targeted... used for the survey}
All American households
976 American households
32% of Americans own two cars
two cars
A survey of 1000 patients at Emory hospital found that 40% cases are heart disease treatment. Identify the population
All Emory hospital patients
1000 Emory hospital patients
40% cases
40 hear disease cases.
A survey of 1000 patients at Emory hospital found that 40% cases are heart disease treatment. Identify the sample.
All Emory hospital patients
1000 Emory hospital patients
40% cases
40 hear disease cases.
What is the response in this experiment?
"Does eating breakfast improve test score?"
eating breakfast or not
the grade you got on the test
what time you get up in the morning
what you eat for breakfast
One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared.
Observational Study
Experiment
A researcher stood at a school parking lot entrance to see if the color of a car is related to the driver not wearing a seatbelt.
Observational Study
Experiment
A professor finds that people who are obese have higher cholesterol levels than those who are not obese.
Observational Study
Experiment
Four groups of randomly selected people are assigned a different diet. After six months, the blood pressures of each group are compared.
Observational Study
Experiment
You want to see if students who have a 4.0 grade point average study more than those who do not.
experiment
observational study
You want to compare the health of students who walk to school to the health of students who ride the bus
experiment
observational study
A researcher randomly assigned boys and girls to each of two groups. One group was assigned to watch a violent television program while the other group watched a nonviolent program. The children's behavior was then recorded for incidences of aggressive behavior. This research method is best characterized as...
experimental
Observation
A psychologist designed a study to test the effects of cell phone use on driving safety. Participants were randomly assigned either to drive an automobile simulator while talking to a friend on a cell phone or to drive a simulator without talking on a phone.
Which type of research does the scenario describe?
Experiment
Observation
To test the effects of breakfast on grades I ask my students if they ate breakfast and then compare the breakfast eaters grades to the non-breakfast eaters.
This is an example of:
Observational study
Experiment
Rats with cancer are divided into two groups. One group receives 5 milligrams of a medication that is thought to fight cancer and the other receives 10 mg. After 2 years, the spread of cancer is measured.
Observational Study
Experiment
Which is one of the main differences between experiments and observational studies?
There is a response variable in an experiment, but not in an observational study.
There is at least one explanatory variable in an experiment, but not in an observational study.
An experiment requires blocking, while an observational study does not.
An experiment can be used to establish a causal relationship, but an observational study cannot.
Observational studies require larger samples than experiments.
Which of the following is a key distinction between well designed experiments and observational studies?
More subjects are available for experiments than for observational studies.
Ethical constraints prevent large-scale observational studies.
Experiments are less costly to conduct than observational studies.
An experiment can show a direct cause-and-effect relationship, whereas an observational study cannot.
Tests of significance cannot be used on data collected from an observational study.
One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared. What is the explanatory variable?
herbal supplement/placebo
number of illnesses
A researcher stood at a school parking lot entrance to see if the color of a car is related to the driver not wearing a seatbelt. What is the response variable?
car color
wearing seatbelt or not
A professor finds that people who are obese have higher cholesterol levels than those who are not obese. What is the explanatory variable?
obesity
cholesterol levels
Four groups of randomly selected people are assigned a different diet. After six months, the blood pressures of each group are compared. What is the response variable?
diet
blood pressure
Researchers were interested in the relationship between farmers’ approach to their cows and the cows’ milk yield. After surveying a random sample of 120 farmers, the researchers found that on farms where cows were called by name, milk yield was 258 liters higher on average than on farms where this was not the case.
Can we conclude that calling the cows by name caused the cows to produce more milk? Why?
Yes, because the sample size was large
Yes, because the farmers were randomly selected
Not necessarily, because the sample size was too small
Not necessarily, because this wasn't an experiment
To check the effect of hot temperatures on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a warm car in the sun for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before the breakage is measured on each rubber band, and the mean for the hot bands is compared to the mean for the others. Is this a good experimental design?
No, because the means are not proper statistics for comparison.
No, because more than two brands should be used.
No, because more temperatures should be used.
No, because temperature is confounded with brand.
Yes
Which example shows a CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)
It rained and the ground is wet.
Ice cream sales increase as temperature increases.
Which example shows CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)
I put water in the freezer and now I have ice.
The alarm clock went off and I woke up.
Temperature and the amount of people at the beach.
Which example shows CAUSATION? (Which one CAUSED the other to happen.)
Rainfall and time spent reading.
Eating more butter and increased divorce rates.
It started raining and the baseball game was delayed.
Which example shows CAUSATION? (Which one CAUSED the other to happen.)
High social media usage and reduced grades.
Car ran out of gas and being stranded on the side of the road.
Recess time and number of friends.
Which example shows CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)
I put water in the freezer and now I have ice.
The alarm clock went off and I woke up.
Temperature and the amount of people at the beach.
Which example shows a CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)
It rained and the ground is wet.
Ice cream sales increase as temperature increases.
If one factor is responsible for change in another factor then it means there is causation.
True or False
True
False
Which one of these examples is NOT an example of CAUSATION?
Kryptonite causes Superman to lose all his powers.
Temperatures of less than 32˚F cause water to freeze.
Umbrellas cause rainstorms.
Stepping on the gas pedal causes a car to move faster.
Correlation or Causation: the number of bus stops increases, the number of car sales decreases?
Correlation
Causation
Correlation or Causation: the speed you drive and the amount of fuel you use?
Correlation
Causation
Correlation or Causation: when it rains several inches, the water level of a lake increases?
Correlation
Causation
Correlation or Causation: when ice cream sales increase, incidents of sunburn increase?
Correlation
Causation
Correlation or Causation: when the amount of sugar in a quart of apple juice is reduced, there are fewer calories in each serving?
Correlation
Causation
when there is more protein in an athlete's diet, the athlete scores more points in a game
Correlation
Causation
