stats chapter 2
The lack of a linear relationship between two quantitative variables is represented by the correlation, r, with values
equal to 0
Malaria is a leading cause of infectious disease and death worldwide. It is also a popular example of a vector-borne disease that could be greatly affected by the influence of climate change. The scatterplot shows total precipitation (in mm) in select cities in West Africa on the x-axis and the percent of people tested positive for malaria in the select cities on the y-axis in 2000. There are influential points in the scatterplot.
true
Time plots are special scatterplots where the explanatory variable, x, is a measure of time
true
Which one of the following statements is (are) true?
None of the above
Do creative people make better teachers? Ten teachers at a large university were given a creativity test (scores range from 0 to 20, with higher scores indicating greater creativity) and were evaluated regarding teaching performance by students and peers (a score of 100 indicates an average performance, and larger scores indicate better performance). Here are the creativity scores and teaching performance scores are given below. We want to investigate if creative people tend to perform better with regard to teacher evaluations. Which of the following is a proper scatterplot of these data given the goals of the study?
a
Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of 5 wild male longtailed finches. Here are the data: Which of the following scatterplots is a correct representation of the data?
a
Consider the following scatterplot of the weight of newborn babies (in grams) versus their length (in centimeters). A plausible value for the correlation between weight and length is
+0.8
I wish to determine the correlation between the height (in inches) and weight (in pounds) of 21-year-old males. To do this I measure the height and weight of two 21-year-old men. The measured values are: The correlation r computed from the measurements on these males is
-1.0
Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of 5 wild male longtailed finches. Here are the data: The value of the linear correlation coefficient between weight and tail feather length is approximately
.888
For which of the following scatterplots would the correlation be close to 1?
1
Which of the following statements about a scatterplot is most true?
On a scatterplot we look for overall patterns showing the form, direction, and the shape of the relationship
Match the three graphs labeled A, B, and C, with the possible values of the correlation coefficient: Assume all graphs are made of the same scale
Correlation of graph B: .95 Correlation of graph A: -.7 Correlation of graph C: .4
Malaria is a leading cause of infectious disease and death worldwide. It is also a popular example of a vector-borne disease that could be greatly affected by the influence of climate change. The table below is a summary from a linear regression that uses dewpoint (oC) to predict malaria prevalence in West Africa. There is a strong correlation between dewpoint and malaria prevalence in West Africa.
False
Which of the following statements is correct?
If people with larger heads tend to be more intelligent, then we would expect the correlation between head size and intelligence to be positive
Consider the following scatterplot of two variables x and y: What can we conclude from this graph?
The correlation between x and y is close to 0
Which of the following is correct?
The correlation coefficient is a unitless number and always lies between -1.0 and +1.0.
A recent article in an educational research journal reports a correlation of +0.8 between math achievement and overall math aptitude. It also reports a correlation of -0.8 between math achievement and a math anxiety test. Which of the following interpretations is the most correct?
The correlation of +0.8 is just as strong as the correlation of -0.8
Which one of the following statements is true?
The correlation, r, measures the strength of the linear relationship between two quantitative variables.
Which of the following statements is (are) FALSE?
The only relationship that a scatterplot can usefully display is linear with no outliers
Negative linear relationships are represented by values of the correlation, r, that are
less than 0
Malaria is a leading cause of infectious disease and death worldwide. It is also a popular example of a vector-borne disease that could be greatly affected by the influence of climate change. The scatterplot shows total precipitation (in mm) in select cities in West Africa on the x-axis and the percent of people tested positive for malaria in the select cities on the y-axis in 2000. The correlation between precipitation and percent tested positive for malaria is probably close to _____.
zero
If you have two quantitative variables, one way to study them is to use a
Scatterplot
To detect the presence of harmful insects in farm fields, boards covered with sticky material and different colors are placed in the fields and the number of insects trapped is counted. Which of the following is correct?
Side-by-side boxplots could be used to compare the number of insects trapped by color.
A study is conducted to determine if one can predict the weight of a newborn baby based on the number of cigarettes smoked by the mother. Which of the following is correct?
The scatterplot should have the number of cigarettes on the X axis and the birth weight on the Y axis
The graph below is a plot of the fuel efficiency (in miles per gallon, or mpg) of various cars versus the weight of these cars (in thousands of pounds).he points denoted by the plotting symbol × correspond to pick-up trucks and SUVs. The points denoted by the plotting symbol - correspond to automobiles (sedans and station wagons). What can we conclude from this plot?
Trucks tend to be higher in weight than automobiles Trucks tend to get poorer gas mileage than automobiles.
Time plots are special scatterplots where the explanatory variable, x, is a measure of time.
True
When examining a scatterplot for form, you are looking to see if _____.
a, b, c
Below is a plot of the Olympic gold medal winning performance in the high jump (in inches) for the years 1900 to 1996. From this plot, the correlation between the winning height and year of the jump is
about .95
Two variables are positively associated when
above average values of one tend to accompany above average values of the other and vice versa
When examining a scatterplot for strength, you are looking to see
all of the above
Has the soft drink industry changed our drinking habits? The Census Bureau reports U.S. per capita consumption of milk and carbonated soft drinks (in gallons per person per year) between 1980 and 2000: Here are some of the data: Which of the following scatterplots is a correct representation of the data?
b
Malaria is a leading cause of infectious disease and death worldwide. It is also a popular example of a vector-borne disease that could be greatly affected by the influence of climate change. The scatterplot shows total precipitation (in mm) in select cities in West Africa on the x-axis and the percent of people tested positive for malaria in the select cities on the y-axis in 2000. Percent tested positive for malaria is the __________ variable.
b and c
When the explanatory variable is categorical and the response variable is quantitative, what type of plot would be appropriate?
boxplot
Below is a scatterplot of heights (in centimeters) of Spartina alterniflora plants against the amount of sunlight they were given (in minutes). Those plants grown at sea level are represented by a closed circle and those grown on the ISS are shown with an open circle. We conclude that
there is a weak association for both locations
Consider the following scatterplot of two variables X and Y. We may conclude that
he correlation between X and Y is close to 0
Consider the following scatterplot of the infected area of a plant versus the time since a pesticide was applied. The correlation between infected area and time since application
is approximately -0.7
Five strains of the Staphylococcus aureus bacteria were grown at 35 degrees Celsius for either 24 hours or 48 hours. Here are the resulting bacterial counts for each condition. The value of the correlation between bacterial count after 24 hours and bacterial count after 48 hours
is approximately 0.89
ird species from temperate regions must cope with relatively short breeding seasons. A study examined the relationship between blood testosterone level (ng/ml) and the duration of the egg-laying period (months) in temperate bird species. The scatterplot below displays this relationship, after taking the logarithm of each variable. The correlation r would have
no units. Correlation is a unitless quantity
A simple random sample of eight drivers was selected. All eight drivers are insured with the same insurance company, and all have similar auto insurance policies. The following table lists their driving experiences (in years) and monthly auto insurance premiums: The correlation coefficient between driving experience and monthly auto insurance premium is r = -0.775. If we would switch the role of explanatory and response variables, what would happen to the correlation coefficient?
nothing
Is it possible to predict a student's score on the midterm exam in a statistics course from the number of hours the student spent studying for the exam? To explore this, the teacher of the course asks students how many hours they spent studying for the exam and then makes a scatterplot of the time students spent studying and their scores on the exam. In making the scatterplot, the teacher should
plot time spent studying for the exam on the horizontal axis
When water flows across farm land, some of the soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (in liters per second) on the amount of soil washed away (in kilograms). The data are given in the following table. The association between flow rate and amount of eroded soil is
positive
Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of 5 wild male longtailed finches. Here are the data: If the measurements were switched so that tail length was treated as an explanatory rather than a response variable, then the correlation would
remain unchanged because correlation doesn't depend on which variable is explanatory
A major study examined the relationship between cause of death (heart attack, cancer, stroke, accident, etc.) and age. A good way to graphically represent the relationship is with
side-by-side boxplots
The owner of a winery collects data on competing wineries every year. He would like to predict the gross sales (in number of cases) from the size of the wineries (in acres). The variable ________ is the explanatory variable in this study
size of the winery
The volume of oxygen consumed (in liters per minute) while a person is at rest and while he or she is exercising (running on a treadmill) was measured for each of 50 subjects. The goal is to determine if the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below. The scatterplot suggests
that both a and b are true.
The Columbus Zoo conducts a study to determine whether a household's income can be used to predict the amount of money the household will give to the zoo's annual fund drive. The response variable in this study is
the amount of money a household gives to the zoo's annual fund drive
Has the soft drink industry changed our drinking habits? The Census Bureau reports U.S. per capita consumption of milk and carbonated soft drinks (in gallons per person per year) between 1980 and 2000: Here are some of the data: We conclude that
the association between milk and soda per capita consumption is clearly curved
Consider the following scatterplot of two variables X and Y. We may conclude that
the correlation between X and Y is close to 0.
