Question 1

For a sample of 15 rural counties in one state,a researcher has collected information about the rate of deaths due to traffic accidents per 1,000,000 population and the percentage of the population which consists of males,age 16 to 25.For these variables,find the least squares regression line and compute r and r squared.Write a sentence or two summarizing and explaining your results.
 $\begin{array}{|l|l|l|}
\hline & \text { RATE OF  } & \text { \% OF POPULATION } \
\hline \text { TOUNTY } & \text { TRAFFIC DEATHS } & \text { YOUNG MALES } \
\hline \mathrm{A} & 15 & 4 \
\hline \mathrm{B} & 16 & 5 \
\hline \mathrm{C} & 22 & 10 \
\hline \mathrm{D} & 23 & 9 \
\hline \mathrm{E} & 20 & 8 \
\hline \mathrm{F} & 25 & 11 \
\hline \mathrm{G} & 18 & 2 \
\hline \mathrm{H} & 15 & 6 \
\hline I& 19 & 12 \
\hline J&10 & 3 \
\hline K&9 & 2 \
\hline L&18 & 15 \
\hline M&15 & 9 \
\hline N& 24 & 16 \
\hline O&9 & 3 \
\hline
\end{array}$

Accepted Answer

The answer of For a sample of 15 rural counties...

Question 2

If we fail to reject the null hypothesis in a test of significance for a Pearson's r,we conclude that
A)there is a negative association between the variables.
B)no inference can be made about the relationship of the two variables in the population.
C)the relationship exists but its direction and strength are unknown.
D)the variables are related in the population.

Accepted Answer

If we fail to reject the null hypothesis in a test of significance for a Pearson's r, we cannot make any inference about the relationship of the two variables in the population. This means that we do not have enough evidence to conclude whether the variables are related or not.

Question 3

In addition to random sampling,interval-ratio level of measurement,and a normal sampling distribution,model assumptions for testing Pearson's r for significance include
A)bivariate normal distributions.
B)a linear relationship.
C)uniformity in the variance of the Y scores around the regression line for all values of X.
D)all of the above

Accepted Answer

The model assumptions for testing Pearson's r for significance are bivariate normal distributions, a linear relationship, and uniformity in the variance of the Y scores around the regression line for all values of X. Therefore, the best choice is D, which includes all of these assumptions.

Question 4

One important limitation of the study of poverty and crime reported in the text is
A)the variables were nominal.
B)the sample was non-random.
C)prediction is not the same thing as association.
D)correlation is not the same thing as causation.

Accepted Answer

Correlation is not the same thing as causation. The study reported in the text only found an association between poverty and crime, but it cannot prove that poverty directly causes crime. There may be other variables or factors that contribute to both poverty and crime, and the relationship between the two may be more complex than a simple cause-and-effect connection. Therefore, it is important to exercise caution when interpreting and applying the findings of such studies.

Question 5

Dummy variables make it possible to include ____ in regression analysis.
A)nominal variables
B)variables measuring intelligence
C)interval-ratio variables
D)variables with more than two scores

Accepted Answer

Dummy variables are specifically used to include nominal variables in regression analysis.

Question 6

A researcher reports a Pearson r of .57 between gender (female = 0,males = 1) and involvement in juvenile delinquency.Which of the following is an appropriate interpretation?
A)females are more delinquent
B)there is no relationship between the variables
C)delinquency increases as gender "increases"
D)only males were delinquent

Accepted Answer

The Pearson r of .57 indicates a positive relationship between gender (coded as 0 for females and 1 for males) and involvement in juvenile delinquency. This means that as gender "increases" (i.e., goes from female to male), delinquency tends to increase as well. However, it is important to note that this does not necessarily mean that females are not delinquent at all or that only males are delinquent.

Question 7

In the study reported in the text,the Pearson's r between the measures of poverty and crime was 0.54.Which of the following is a reasonable interpretation of this result?
A)poverty causes crime
B)crime causes poverty
C)as poverty increases,crime decreases
D)there is a moderate,positive correlation between poverty and crime

Accepted Answer

A Pearson's correlation coefficient of 0.54 indicates a moderate, positive correlation between poverty and crime. However, correlation does not imply causation so it is not appropriate to conclude that poverty causes crime or vice versa based on this result alone.

Question 8

If we calculate an r of .60,the proportion of the variation of Y that is explained by X is
A).36.
B).40.
C).60.
D).64.

Accepted Answer

The proportion of the variation of Y that is explained by X in a correlation is found by squaring the correlation coefficient (r), which in this case is .60. So, .60 squared equals .36.

Question 9

In a study of the relationship between geographical mobility (number of times a person has changed residences)and number of friends,Pearson's r² is reported as .40.Which of the following would be a correct interpretation? A)Mobility explains 16% of the variation in number of friends. B)There is a strong positive relationship between number of friends and mobility. C)As mobility increases,number of friends decreases. D)Mobility explains 40% of the variation in number of friends.

Accepted Answer

Pearson's r is a measure of the strength of linear association between two variables. The possible values of r range from -1 to 1, with values closer to -1 or 1 indicating a stronger linear relationship. A value of 0 indicates no linear relationship. In this case, r = .40, which means there is a moderate positive linear relationship between geographical mobility and number of friends. The square of the correlation coefficient (r²) represents the proportion of variation in one variable that is explained by the other variable. Therefore, r² = .16, meaning that 16% of the variation in number of friends can be explained by geographical mobility. So, option D is the correct interpretation.

Question 10

When testing Pearson's r for significance,the null hypothesis is that
A)there is no difference between the variables in the population from which the sample was drawn.
B)there is no linear association between the variables in the population from which the sample was drawn.
C)there is no difference between the sample and the population from which the sample was drawn.
D)r = 1.00.

Accepted Answer

The null hypothesis when testing Pearson's r for significance is that there is no linear association between the variables in the population from which the sample was drawn. The alternative hypothesis is that there is a significant linear association between the variables.

Question 11

The text reported information about the relationship between crime and poverty.The sample used was
A)1000 randomly selected Americans.
B)a group of inmates from a federal penitentiary.
C)a large group of high school students.
D)the fifty states.

Accepted Answer

The text mentions "a study of the fifty states" and the analysis of crime and poverty rates across those states. Thus, it is most likely that the sample used was the fifty states themselves.

Quiz 15: Association Between Variables Measured at the Interval-Ratio Level

If we fail to reject the null hypothesis in a test of significance for a Pearson's r,we conclude that

In addition to random sampling,interval-ratio level of measurement,and a normal sampling distribution,model assumptions for testing Pearson's r for significance include

One important limitation of the study of poverty and crime reported in the text is

Dummy variables make it possible to include ____ in regression analysis.

A researcher reports a Pearson r of .57 between gender (female = 0,males = 1) and involvement in juvenile delinquency.Which of the following is an appropriate interpretation?

In the study reported in the text,the Pearson's r between the measures of poverty and crime was 0.54.Which of the following is a reasonable interpretation of this result?

If we calculate an r of .60,the proportion of the variation of Y that is explained by X is

In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends,Pearson's r² is reported as .40.Which of the following would be a correct interpretation?

When testing Pearson's r for significance,the null hypothesis is that

The text reported information about the relationship between crime and poverty.The sample used was