Exam 2 Chapter 5 E

Consider Figure 5.40. According to this diagram, life expec-tancy in Brazil is about

62 years

What is a​ correlation? Give three examples of pairs of variables that are correlated.

A correlation exists between two variables when higher values of one variable consistently go with higher or lower values of another variable.

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. Explain your reasoning.

The age of a person and time spent on social networking sites To measure​ age, the unit years since birth might be used. To measure​ time, the unit hours might be used. What​ correlation, if​ any, is there between the​ variables? There is a negative correlation because time spent on social networking sites tends to increase when age decreases.

Give three examples of pairs of variables that are correlated. Select the correct answer below.

amount of smoking and lung​ cancer, height and weight of​ people, price of a good and demand of the good

The statement makes sense. ​Originally, a negative correlation was suspected. Since no correlation was​ found, there is apparently no relationship between the variables.

makes sense a negative no

Define negative correlation. Choose the correct answer below.

Negative correlation means that two variables tend to change in opposite​ directions, with one increasing while the other decreases.

Define no correlation. Choose the correct answer below.

No correlation means that there is no apparent relationship between the two variables.

When we say that X is correlated with Y, we mean that

x causes y

Briefly describe each of the six guidelines for establishing causality. Give an example of the application of each guideline. The first guideline states that one should look for situations where the effect is correlated with the suspected​ cause, even when other factors vary.

.Give an example of the first guideline. Select the correct answer below. When checking to see if smoking causes​ cancer, let groups of smokers and​ non-smokers be completely random to see if lung cancer occurs more in the smoking group than the​ non-smoking group.

The second guideline states that among groups that differ only in the presence or absence of the suspected​ cause, one should check that the effect is similarly present or absent.

Give an example of the second guideline. Select the correct answer below. When checking to see if smoking causes​ cancer, look at two groups as identical as​ possible, with one group being smokers and the other group being​ non-smokers.

Define and distinguish among positive​ correlation, negative​ correlation, and no correlation. How do we determine the strength of a​ correlation? Define positive correlation. Choose the correct answer below.

Positive correlation means that both variables tend to increase​ (or decrease) together.

How do we determine the strength of a​ correlation?

The more closely two variables follow the general​ trend, the stronger the correlation​ (which may be positive or​ negative).

I found a nearly perfect positive correlation between variable A and variable B and therefore was able to conclude that an increase in variable A causes an increase in variable B.

The statement does not make sense because a correlation alone is not enough evidence to establish causality.

Determine whether the statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. There is a strong negative correlation between the price of tickets and the number of tickets sold. This suggests that in order to sell a lot of​ tickets, the price should be lowered.

The statement makes sense. To increase the ticket​ sales, the price should be decreased since there is a strong negative correlation.

Consider the following statement about a correlation. State the correlation clearly​ (for example, there is a positive correlation between variable A and variable​ B). Then state whether the correlation is most likely due to​ coincidence, a common underlying​ cause, or a direct cause. Explain your answer. Automobile gas mileage decreases with tire pressure.

There is a positive correlation between gas mileage and tire pressure.

Consider the following statement about a correlation. State the correlation clearly​ (for example, there is a positive correlation between variable A and variable​ B). Then state whether the correlation is most likely due to​ coincidence, a common underlying​ cause, or a direct cause. Explain your answer. Over the past 30​ years, data show that the number of games won by Major League baseball teams increased with team payroll.

There is a positive correlation between a​ team's payroll and games won. This could be a direct cause since a baseball team is likely to get paid more the better they do.

Consider the following statement about a correlation. State the correlation clearly. Then state whether the correlation is most likely due to a​ coincidence, a common underlying​ cause, or a direct cause. Explain your answer. Over the past three​ decades, the number of miles of freeways in Los Angeles has​ grown, and traffic congestion has worsened.

There is a positive correlation between the number of miles of freeways and the traffic congestion in Los Angeles. The correlation is most likely due to the common underlying cause of Los Angeles having a very large population.

Consider the scatterplot to the right. a. State whether the diagram shows a positive​ correlation, a negative​ correlation, or no correlation. If there is a positive or negative​ correlation, is it strong or​ weak? b. Summarize any conclusions that can be drawn from the diagram.

There is a strong negative correlation

Consider the scatterplot to the right. a. State whether the diagram shows a positive​ correlation, a negative​ correlation, or no correlation. If there is a positive or negative​ correlation, is it strong or​ weak? b. Summarize any conclusions that can be drawn from the diagram.

There is a weak positive correlation.

Determine the possible explanation for the correlation. Choose the correct answer below.

This correlation is due to a direct cause because more gasoline is needed to roll a tire with lower pressure.

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. Explain your reasoning. HeightHeight and how frequently a person attends countrycountry concerts

To measure height​, the unit feet might be used. To measure the frequency a person attends country ​concerts, the unit number of attendances might be used. What​ correlation, if​ any, is there between the​ variables? The variables are not correlated.

For the following pair of​ variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are​ correlated, state whether the correlation is positive or negative. Explain your reasoning. Latitude and the average high temperature in June

To measure​ latitude, the unit degrees of latitude might be used. To measure​ temperature, the unit degrees Fahrenheit might be used. What​ correlation, if​ any, is there between the​ variables? There is a negative correlation because the average high temperature in June tends to increase when latitude decreases.

The fourth guideline states that if the effect might be produced by other potential​ causes, make sure the effect still remains after accounting for these other potential causes.

When checking to see if smoking causes​ cancer, let the group of smokers vary between people of different ethnicities and genetic background to see if lung cancer is still more prevalent among smokers than​ non-smokers.

The third guideline states to look for evidence that larger amounts of the suspected cause produce larger amounts of the effect.

When checking to see if smoking causes​ cancer, look at those who smoke a lot and those who only smoke a little and compare the incidents of lung cancer.

The fifth guideline states that the suspected cause should be tested with an experiment.

When checking to see if smoking causes​ cancer, test the effects of cigarettes on lung tissue or animals.

The sixth guideline states that the physical mechanism by which the suspected cause produces the effect should be determined.

When checking to see if smoking causes​ cancer, try to find what it is in cigarettes that causes cells to mutate and cause cancer.

The accompanying table gives the literacy rate and the infant mortality rate​ (per 1,000​ births) for ten countries. Complete parts​ (a) though​ (c). Click the icon to view the literacy rate and infant mortality rate data.

b. State whether the two variables appear to be​ correlated, and if​ so, state whether the correlation is​ positive, negative,​ strong, or weak. The two variables appear to have strong negative correlation. c. Suggest a reason for the correlation or lack of correlation Countries with higher literacy rates likely have more money and good health care for infants so they have low infant mortality rates.

The following table gives the average hours of traditional​ (network and​ cable) television watched per week in five age categories. For the age​ categories, use the data points​ 6, 15,​ 21, 40, 65. Complete parts​ (a) through​ (c).

b. State whether the two variables appear to be​ correlated, and if​ so, state whether the correlation is​ positive, negative,​ strong, or weak. The two variables appear to have strong positive correlation. c. Suggest a reason for the correlation or lack of correlation. As people get​ older, they have more free time and can watch more TV.

The following table gives the average teacher salary and the expenditure on public education per pupil for ten places. Complete parts a though c.

b. State whether the two variables appear to be​ correlated, and if​ so, state whether the correlation is​ positive, negative,​ strong, or weak. A. The two variables appear to have strong positive correlation. c. Suggest a reason for the correlation or lack of correlation. States more focused on education are more likely to pay teachers more and spend more​ per-pupil.