U1: Data Displays
Researchers record the number of years of education, what classes were taken, and the GPA for a sample of 1463 adults. How many quantitative and categorical variables were recorded?
3 quantitative, 0 categorical.
3 quantitative, 1 categorical.
2 quantitative, 1 categorical.
1 quantitative, 2 categorical.
2 quantitative, 1 categorical.
Which of the following is a statistical question?
What is the height of Mount Everest?
How many goals did Pelé score in the 1970 World Cup?
How many minutes do students at our school typically spend on homework each night?
How much did the Johnson family spend on gas last week?
How many minutes do students at our school typically spend on homework each night?
Consider many cities around the world. There is a strong, positive correlation between the number of coffee shops per 10,000 people (x) and the average number of books read per person per year (y). Does this mean that building more coffee shops in a city will make people read more books?
No. This conclusion would only be reasonable if the correlation were negative.
No. The positive correlation only shows that cities with more educated populations tend to have both more coffee shops and more reading.
Yes. Because the correlation is positive, adding coffee shops will increase the number of books people read.
Yes. Because the correlation is strong, more coffee shops cause people to read more books.
No. The positive correlation only shows that cities with more educated populations tend to have both more coffee shops and more reading.
During her tennis career, Serena serves first-serve points successfully about 78% of the time. Suppose she is currently a 0.78 first-serve player. Serena successfully serves 10 first serves in a row. What is the probability she will make her next first serve?
0.22
0.78
0.50
0.10
0.78
Determining how many wind turbines in a new wind farm will produce substantial energy is important when deciding whether to expand the project. Below are the estimated total electricity outputs (in thousands of megawatt-hours) from all 36 turbines in a particular wind farm. The data are listed in ascending order.
3 12 18 20 21 24 28 30 32 32 34 35 36 38 40 41 43 45 46 48 50 52 54 56 58 60 63 65 68 70 75 78 85 110
Alex says that 3 is a low outlier.
Jordan says that 110 is a high outlier.
Who is correct? Justify your answer using an appropriate outlier rule (such as the IQR method).
Alex is correct.
Jordan is correct.
Both Alex and Jordan are correct.
Neither Alex nor Jordan is correct.
Jordan is correct.
For which variable would it be more appropriate to use a bar chart instead of a histogram to display the distribution?
Favorite day of the week
The number of times to exercise in a week
Class size
Square footage of the house
Favorite day of the week
A state transportation department wanted to estimate the percentage of residents who primarily use public transportation to commute to work. They randomly called phone numbers until they obtained responses from 1200 adults in the state. In the survey, 34% of respondents said they primarily use public transportation. In reality, only 18% of adults in the state primarily use public transportation.
Which of the following best explains the difference between the two percentages?
The difference is due to sampling variability. Results from a random sample will not exactly match the true population value every time.
The difference is due to response bias. Respondents are intentionally giving inaccurate answers about their commuting habits.
The difference is due to undercoverage. The survey included only adults and excluded students who also commute.
The difference is due to nonresponse. Adults who commute by public transportation are more likely to be available to answer the survey than those who do not.
The difference is due to nonresponse. Adults who commute by public transportation are more likely to be available to answer the survey than those who do not.
A researcher records the daily screen time (in hours) and the amount of sleep (in hours) for 50 teenagers. The correlation is r = –0.534. What does this tell us?
Teenagers who spend more time on screens tend to get less sleep, and the relationship is moderately strong.
53.4% of the variation in sleep is accounted for by screen time.
For each additional hour of screen time, predicted sleep decreases by 0.534 hours.
The relationship between screen time and sleep is fairly strong and positive.
Teenagers who spend more time on screens tend to get less sleep, and the relationship is moderately strong.
A random sample of 160 high school students in grades 10 and 11 was selected. The two-way table summarizes each student’s grade level and their response to the question “Do you play a musical instrument?” Suppose we choose a student from this sample at random. What is the probability that the student does not play an instrument?
45/160 B. 85/160 C. 75/160 D. 45/75
C. 75/160
A high school wants to find out how many students participate in after-school sports. Which method is most likely unbiased?
Stand outside the gym after practice and ask students if they participate in sports.
Ask the PE teachers to give the survey to their own favorite students.
Randomly select students from the school roster and ask them if they participate in sports.
Send a voluntary online survey to the entire student body.
Randomly select students from the school roster and ask them if they participate in sports.
Thirty-five students completed a science quiz worth a maximum of 50 points. The teacher recorded the class results and organized the scores into the following stem-and-leaf plot. Calculate the median and interquartile range of this distribution.
Stem | Leaf
2 | 4 5 7 8
3 | 0 1 1 2 3 4 4 5 6 7 7 8 9
4 | 0 0 1 2 3 4 5 6 7
Key: 4 | 0 = 40 points
Median = 36.5 and IQR = 41-31=10
Which of the following best describes a defining feature of a designed experiment?
The investigator records outcomes without influencing the participants.
The investigator randomly assigns individuals to different treatment conditions.
The individuals describe their own actions or responses.
The investigator studies individuals in their usual, everyday setting.
The investigator randomly assigns individuals to different treatment conditions.
The following statement contains an error. Explain what is wrong:
"The correlation between daily temperature (°F) and ice cream sales ($) is r = $3."
One variable is categorical, and the correlation r is for two quantitative variables. The term correlation is not appropriate here.
Both variables are categorical, and the correlation r is for two quantitative variables. The term correlation is not appropriate here.
The correlation r should not have units.
The correlation is less than 1. This is wrong because the correlation r must be greater than 1.
The correlation r should not have units.
A random sample of 160 high school students in grades 10 and 11 was selected. The two-way table summarizes each student’s grade level and their response to the question “Do you play a musical instrument?”
Suppose we choose a student from this sample at random. What is the probability that the student is in 11th grade or plays an instrument?
165/160 B. 95/160 C. 130/160 D. 115/160
D. 115/160
Which of the following correlation coefficients describes the weakest correlation?
r= -0.4
r= -0.9
r=0.9
r=0.2
r=0.2
Calculate and interpret the standard deviation of the following data set.
Stem | Leaf
2 | 4 5 7 8
3 | 0 1 1 2 3 4 4 5 6 7 7 8 9
4 | 0 0 1 2 3 4 5 6 7
Key: 4 | 0 = 40 points
6.49; The typical distance away from the mean is 6.49.
A researcher studies study-habit patterns among high school students attending private schools in large cities. To which population would it be most appropriate to generalize the results of this study?
All high school students attending private schools in large cities.
All high school students in large cities.
All private school students.
All students who attend private schools.
All high school students attending private schools in large cities.
A researcher wants to study whether receiving compliments can improve a person’s mood. She selects individuals walking in a park in the afternoon. Each person is given a set number of compliments (ranging from 1 to 5) and is asked to pay attention to how they feel afterward. She calls each person later in the day to rate their mood on a scale from 1 to 10. The table shows the number of compliments and the mood rating:
Number of Compliments
1
3
2
5
4
2
5
3
Mood Rating
5
7
6
9
8
7
10
8
21. Use technology to calculate the equation of the least-squares regression line relating 𝑦 = mood rating to 𝑥 = Number of Compliments.
y=4.24x+1.04
y= -1.04x+4.24
y=1.04x-4.24
y=1.04x+4.24
y=1.04x+4.24
A random sample of 160 high school students in grades 10 and 11 was selected. The two-way table summarizes each student’s grade level and their response to the question “Do you play a musical instrument?”
Suppose we choose a student from the sample at random. What is the probability that the student is a 10th grader, given that the student plays an instrument?
35/85 B. 35/80 C. 35/160 D. 50/160
35/85
Suppose you flip a fair coin 8 times. Find the probability of getting at least one head.
0.0039 B. 0.9961 C. 0.5000 D. 0.8750
B. 0.9961
Based on the shape and spread shown in the graph, which of the following conclusions can reasonably be made about the distribution?
The distribution is left-skewed.
The range of the distribution is at most $90.
The variability of the data suggests a standard deviation greater than 60.
The mean is more than the median.
The mean is more than the median.
A study found that children who drank a lot of soda were more likely to have cavities than children who drank little or no soda. However, children with poor dental hygiene habits are also more likely to drink soda frequently. This makes it difficult to determine whether the cavities are caused by soda consumption or by poor dental hygiene. This is an example of:
a response variable
the placebo effect
Confounding
bias
Confounding
A researcher wants to study whether receiving compliments can improve a person’s mood. She selects individuals walking in a park in the afternoon. Each person is given a set number of compliments (ranging from 1 to 5) and is asked to pay attention to how they feel afterward. She calls each person later in the day to rate their mood on a scale from 1 to 10. The table shows the number of compliments and the mood rating:
Number of Compliments
1
3
2
5
4
2
5
3
Mood Rating
5
7
6
9
8
7
10
8
Calculate and interpret the correlation coefficient.
The correlation coefficient of r = 0.9473 indicates that the linear relationship between the number of complements and the mood rating of college students is positive and moderately strong.
A random sample of 160 high school students in grades 10 and 11 was selected. The two-way table summarizes each student’s grade level and their response to the question “Do you play a musical instrument?”
Suppose we choose a student from the sample at random. What is the probability that the student is a 10th grader and plays an instrument?
35/85 B. 35/80 C. 35/160 D. 50/160
C. 35/160
Suppose we choose a student from this sample at random. Which of the following is true about the events “Student is an 11th-grader” and “plays an instrument”?
The events are not mutually exclusive, but they are independent.
The events are mutually exclusive, but they are not independent.
The events are not mutually exclusive, nor are they independent.
The events are both mutually exclusive and independent.
The events are not mutually exclusive, nor are they independent.