Chapter 7: Causal Relationship and Bivariate Analysis

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What is the primary limitation of a bivariate analysis in establishing a causal relationship?

It is only used for hypothesis testing.

It only considers continuous variables.

It only considers categorical variables.

It only considers two variables. (correct)

What type of hypothesis test is used when there is a continuous dependent variable and a categorical independent variable?

Difference of Proportions test

ANOVA test

Difference of Means test (correct)

T-test

In a Difference of Means test, what is used to make inferences about the population?

Sample means and standard deviations (correct)

Sample means and variances

Population means and standard errors

Population means and variances

What is a characteristic of a parliamentary system in a democratic regime?

The lower house of the legislature is the most powerful branch of government. Signup and view all the answers

What is the purpose of hypothesis testing in the context of a Difference of Means test?

To determine if the sample means are significantly different from what we would expect if there were no relationship Signup and view all the answers

What is the current status of the causal claim in the example given?

The causal claim is supported but not yet established Signup and view all the answers

What is the formula for the standard error of the difference between two means?

√((n1 - 1)s12 + (n2 - 1)s22) / (n1 + n2 - 2) Signup and view all the answers

What is the purpose of calculating the degrees of freedom in a t-test?

To gain confidence in an observed pattern as the amount of data increases Signup and view all the answers

What is the formula for calculating the degrees of freedom in a difference of means t-statistic?

n1 + n2 - 2 Signup and view all the answers

What is the purpose of the t-statistic?

To obtain the p-value Signup and view all the answers

What is the use of the critical values table for t-statistic?

To determine the minimum t-value needed to achieve a targeted p-value Signup and view all the answers

What is the relationship between the degrees of freedom and the confidence in an observed pattern?

As the degrees of freedom increase, confidence in the pattern increases Signup and view all the answers

What is the primary purpose of calculating a t-statistic for a correlation coefficient?

To assess if the relationship is statistically significant. Signup and view all the answers

What is the degrees of freedom (df) for the t-statistic calculation?

n-2 Signup and view all the answers

What is the value of the correlation coefficient (r) in the example calculation?

0.57366207 Signup and view all the answers

What is the formula for calculating the t-statistic for a correlation coefficient?

√(r / (√(n-2)) * (1 - r^2)) Signup and view all the answers

What is the calculated t-value in the example calculation?

3.961852291 Signup and view all the answers

What does the t-statistic help us determine in the context of correlation analysis?

Whether the correlation is statistically significant. Signup and view all the answers

What does the covariance calculation tell us about the relationship between the independent and dependent variables?

The direction of the relationship Signup and view all the answers

What is the value of degrees of freedom in this hypothesis test?

32 Signup and view all the answers

What is the critical t-value at a p-value of 0.05 for a two-tailed test with 30 degrees of freedom?

1.697 Signup and view all the answers

What is the value of the correlation coefficient if all points in the plot line up perfectly on a straight, negatively sloping line?

-1 Signup and view all the answers

What can be said about the correlation coefficient when it is equal to 0?

There is no correlation Signup and view all the answers

What is the probability of observing the correlation between the two variables due to random chance?

Less than 0.001 Signup and view all the answers

What is the range of values for the correlation coefficient?

-1 to 1 Signup and view all the answers

Which of the following tests is used to analyze the correlation between two continuous variables?

Correlation Coefficient (Pearson’s r) Signup and view all the answers

What does a correlation coefficient of 1 indicate?

A perfect positive relationship Signup and view all the answers

What is the next topic to be covered in the book?

Bivariate regression analysis Signup and view all the answers

What is the purpose of using the Pearson's Correlation Coefficient?

To assess the confidence level that the relationship is different from the population of interest Signup and view all the answers

How many methods for conducting bivariate hypothesis tests are introduced in this chapter?

3 Signup and view all the answers