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.

Accepted Answer

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

Question 2

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 for 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. This means that there is no significant correlation between the two variables. Dtype:short_answer

Question 3

The conditional mean of Y for any value of X is found by________.
A) adding the Y scores for the specific value of X and dividing by N.
B) adding all the Y scores and dividing by X.
C) subtracting the mean of Y from the overall mean of X.
D) Any of the answer choices

Accepted Answer

The conditional mean of Y for any value of X is found by adding the Y scores for the specific value of X and dividing by N. This is known as the mean of the conditional distribution of Y that corresponds to that specific value of X.

Question 4

In a scatterplot, the point of minimized variation for scores of Y for a given value of X (the independent variable) is________.
A) the sum of the conditional Y scores.
B) the standard deviation of the conditional Y scores.
C) the mean of the conditional Y scores.
D) the predicted Y score.

Accepted Answer

The point of minimized variation for scores of Y for a given value of X is the mean of the conditional Y scores, which is also known as the conditional mean. This means that for a specific value of X, the average score of Y is the point where the variation in scores is at its lowest. This is because the mean of the conditional Y scores represents the best estimate of Y for a given value of X.

Question 5

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

The best choice is D because the study only found a correlation between poverty and crime, but it did not establish causation. This means that poverty may be associated with crime, but poverty does not necessarily cause crime. Other factors may be involved.

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

A Pearson r of .57 indicates a moderate positive relationship between gender and involvement in juvenile delinquency. As the value of gender increases (from 0 to 1, representing females to males), involvement in delinquency also tends to increase. However, this does not necessarily mean that only males were delinquent, and it does not provide information about which gender is more delinquent.

Question 7

Scatterplots give information about the _____________ of a relationship.
A) strength
B) direction
C) linearity
D) All of the answer choices

Accepted Answer

Scatterplots give information about the strength, direction, and linearity of a relationship.

Question 8

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 allow nominal variables (which have categories but no numerical value) to be included in regression analysis by creating binary variables (0 or 1) to represent each category.

Question 9

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 answer choices

Accepted Answer

All of the given choices are model assumptions for testing Pearson's r for significance. Bivariate normal distributions assumption means that the distribution of X and Y are normally distributed. A linear relationship implies that the relationship between X and Y is linear. Uniformity of variance around the regression line means that the variability of Y scores is consistent as X changes. Therefore, all of these assumptions need to be met to test Pearson's r for significance.

Question 10

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 for a Pearson's r, it means that there is not enough evidence to suggest that there is a significant linear relationship between the two variables in the population. Therefore, we cannot make any inference about the relationship of the two variables in the population.

Question 11

If a line is drawn through the conditional means of Y, the line will________.
A) always be perfectly linear.
B) rarely be a perfectly straight line.
C) always be parallel to the horizontal axis.
D) always be parallel to the vertical axis.

Accepted Answer

The line drawn through the conditional means of Y will rarely be a perfectly straight line because there may be variability in the relationship between X and Y within each group or level of the conditional variable. This can result in a non-linear relationship between X and Y within each group, which can translate to a non-linear overall relationship when the conditional means are connected.

Question 12

The text reported information about the relationship between homicide 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 that the sample used was the fifty states, which were analyzed for their homicide rates and poverty levels.

Question 13

In the study reported in the text, the Pearson's r between the measures of poverty and homicide was 0.57. Which of the following is a reasonable interpretation of this result?
A) Poverty causes homicide.
B) Homicide causes poverty.
C) As poverty increases, homicide decreases.
D) There is a moderate, positive correlation between homicide and poverty.

Accepted Answer

The Pearson's r of 0.57 indicates a moderate, positive correlation between homicide and poverty. This means that as levels of poverty increase, so do levels of homicide, but it does not necessarily indicate causation in either direction.

Question 14

A perfect association between variables can be seen on a scatterplot when________.
A) all dots lie an equal distance from the regression line.
B) all dots lie on the regression line.
C) the regression line forms a right angle at its intersection with the X axis.
D) the regression line is parallel to the X axis.

Accepted Answer

When all dots lie on the regression line, it indicates a perfect association between variables. The regression line represents the relationship between the two variables and when all the data points fall on the line, it means that every change in one variable perfectly predicts a change in the other variable.

Question 15

The direction of a relationship between variables can be detected on a scatterplot by considering the angle of the regression line. The relationship is________.
A) positive when the line slopes upward from left to right.
B) positive when the line slopes downward from left to right.
C) negative when the line slopes upward from left to right.
D) negative when the line slopes downward from right to left.

Accepted Answer

The direction of the relationship can be detected by examining the slope of the regression line. A positive slope (sloping upward from left to right) indicates a positive relationship, meaning that as one variable increases, the other variable also tends to increase.

Question 16

In regression analysis, the symbol "a" stands for________.
A) the scores on the Y variable.
B) the slope.
C) the Y intercept.
D) the X intercept.

Accepted Answer

In regression analysis, the symbol "a" represents the Y intercept, which is the value of Y when X equals zero. The slope is represented by the symbol "b", and the X and Y intercepts are typically denoted as "x-int" and "y-int", respectively.

Question 17

The Y intercept is the point where________.
A) the horizontal axis connects to the vertical axis.
B) the regression line crosses the horizontal axis of the scattergram.
C) the regression line meets the conditional mean of Y.
D) the regression line crosses the vertical axis of the scattergram.

Accepted Answer

The Y intercept is the point where the regression line crosses the vertical axis of the scattergram.

Quiz 13: Association Between Variables Measured at the Interval Ratio Level

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

The conditional mean of Y for any value of X is found by________.

In a scatterplot, the point of minimized variation for scores of Y for a given value of X (the independent variable) is________.

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

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?

Scatterplots give information about the _____________ of a relationship.

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

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________.

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

If a line is drawn through the conditional means of Y, the line will________.

The text reported information about the relationship between homicide and poverty. The sample used was________.

In the study reported in the text, the Pearson's r between the measures of poverty and homicide was 0.57. Which of the following is a reasonable interpretation of this result?

A perfect association between variables can be seen on a scatterplot when________.

The direction of a relationship between variables can be detected on a scatterplot by considering the angle of the regression line. The relationship is________.

In regression analysis, the symbol "a" stands for________.

The Y intercept is the point where________.