Chapter 7: Causal Relationship and Bivariate Analysis
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Questions and Answers

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?

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

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

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

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

    <p>The causal claim is supported but not yet established</p> Signup and view all the answers

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

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

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

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

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

    <p>n1 + n2 - 2</p> Signup and view all the answers

    What is the purpose of the t-statistic?

    <p>To obtain the p-value</p> Signup and view all the answers

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

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

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

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

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

    <p>To assess if the relationship is statistically significant.</p> Signup and view all the answers

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

    <p>n-2</p> Signup and view all the answers

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

    <p>0.57366207</p> Signup and view all the answers

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

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

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

    <p>3.961852291</p> Signup and view all the answers

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

    <p>Whether the correlation is statistically significant.</p> Signup and view all the answers

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

    <p>The direction of the relationship</p> Signup and view all the answers

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

    <p>32</p> 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?

    <p>1.697</p> 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?

    <p>-1</p> Signup and view all the answers

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

    <p>There is no correlation</p> Signup and view all the answers

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

    <p>Less than 0.001</p> Signup and view all the answers

    What is the range of values for the correlation coefficient?

    <p>-1 to 1</p> Signup and view all the answers

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

    <p>Correlation Coefficient (Pearson’s r)</p> Signup and view all the answers

    What does a correlation coefficient of 1 indicate?

    <p>A perfect positive relationship</p> Signup and view all the answers

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

    <p>Bivariate regression analysis</p> Signup and view all the answers

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

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

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

    <p>3</p> Signup and view all the answers

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