Statistical Studies
A researcher wants to know whether students at a school prefer online or paper homework. She surveys 300 randomly selected students. What is the population?
All students at the school.
Give two examples of quantitative variables and two examples of categorical variables.
Answers will vary.
A segmented bar graph is used to display the relationship between two categorical variables. What should each complete bar add up to?
100%
A researcher records the number of text messages each student sends in one day. Is this variable discrete or continuous?
Discrete, because the number of text messages is countable and cannot take any value between two whole-number counts.
What high school did I graduate from?
Musselman!!!!!!!
A college basketball coach wants to analyze performance for the players on her team during the season. For the entire season, she records the total number of minutes played, points scored, and rebounds for every player on the team across all games. Which of the following best describes the data collection?
A) A sample, because only basketball players were included.
B) An experiment, because the coach is measuring player outcomes.
C) A census, because data were collected from every player in the team’s population.
D)A retrospective study, because the coach is using historical player data.
C
In a survey of 50 students, 15 chose basketball as their favorite sport. What is the relative frequency of students who chose basketball?
30%
What type of graph displays data where the width of the bars is proportional to the group size?
Mosaic Plot
Which display of quantitative data shows the general shape of a distribution but does not show every individual data value?
Histogram
What color was my shirt yesterday?
Green
A researcher records each student's favorite school subject and number of hours of sleep last night. Classify each variable as categorical or quantitative.
Favorite school subject = categorical; hours of sleep = quantitative.
At a school, 40% of all students prefer math over English. Among students who play a sport, 40% prefer math over English.
Based on this information, does playing a sport appear to be associated with whether a student prefers math or English? Explain.
No. The percentage who prefer math is the same among athletes as it is overall, so knowing whether a student plays a sport does not appear to help predict their preference.
A segmented bar graph compares favorite season for middle school and high school students. The sections of the two bars are almost identical in size.
What does this suggest about the relationship between school level and favorite season?
There is little or no association because the bars are approximately the same.
A researcher has a histogram of a data set. She wants to determine the exact value of every observation using only the histogram.
Can she do it? If not, name two displays that would allow her to see every individual value.
No. A histogram groups observations into intervals, so the exact individual values cannot necessarily be recovered.
How many cats do I have? Give me the name of ONE of them.
Researchers recruit 500 ninth graders and record their current exercise habits. They then follow the students for four years and record their health each year. Is this a prospective or retrospective study? Explain.
Prospective, because the researchers follow the participants forward in time.
Of 100 students surveyed, 30 are freshmen and 12 of those freshmen prefer math.
What percent of the freshmen prefer math, and is this a marginal, joint, or conditional relative frequency?
40%, and a conditional relative frequency
A mosaic plot compares two groups, A and B. The bar for Group A is twice as wide as the bar for Group B. In Group A, 30% chose Option X. In Group B, 60% chose Option X.
Without knowing the actual sample sizes, which group contributed more people who chose Option X, or are they equal? Explain.
They are equal.
A distribution of household incomes is strongly skewed right.
Without calculating anything, which would you expect to be larger: the mean or median? Which measure of center would be more appropriate?
The mean would likely be greater than the median, because the large values in the right tail pull the mean upward.
Who is my favorite NBA player?
A study finds that high school students who eat breakfast every day tend to have higher GPAs than students who do not. A headline says, “Eating Breakfast Causes Students to Get Better Grades.”
Explain if this headline is correct or incorrect and why using statistical reasoning.
It is incorrect due to studies being only able to find association, not causation.
In a survey of 250 students, 32% are juniors. Of the juniors, 45% have a part-time job.
How many students surveyed are juniors AND have a part-time job?
36
Two separate relative-frequency bar graphs compare favorite streaming service for Group A and Group B.
For Group A, 40% chose Netflix.
For Group B, 40% chose Netflix.
A student says:
“The Netflix bars are the same height, so the same number of people in each group chose Netflix.”
Is the student necessarily correct? Explain.
No. Equal bar heights on relative-frequency bar graphs mean the same percentage, not necessarily the same number of people. If the groups have different sample sizes, the counts could be different.
What does SOCV stand for?
Shape, Outliers, Center, Variability
Chicago, Cleveland, Cincy, Vegas,