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Hypothesis Tests for Correlation Coefficient Using TI-85 quiz

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  • What does a correlation coefficient r close to zero indicate about the relationship between two variables?
    It indicates weak or no linear correlation between the two variables.
  • What is the null hypothesis when testing the population correlation coefficient ρ?
    The null hypothesis is that ρ equals zero, meaning there is no linear correlation between the variables.
  • What does the alternative hypothesis state in a two-sided test for correlation?
    It states that ρ is not equal to zero, indicating a linear correlation exists.
  • Which function on the TI-84 calculator is used to test the correlation coefficient?
    The LinReg t-test function is used to test the correlation coefficient.
  • What does a p-value less than the alpha level indicate in hypothesis testing for correlation?
    It indicates that we reject the null hypothesis and conclude there is statistically significant linear correlation.
  • If the alternative hypothesis is ρ > 0, what type of correlation are you testing for?
    You are testing for a positive linear correlation.
  • What should you do if the p-value is greater than the alpha level in a correlation test?
    You fail to reject the null hypothesis, meaning there is not enough evidence for a linear correlation.
  • What is the first step when using the TI-84 to test for correlation?
    The first step is to enter your data into lists, typically L1 and L2.
  • What does the sample correlation coefficient r represent in the output of the LinReg t-test?
    It represents the strength and direction of the linear relationship in your sample data.
  • Why is it important to choose the correct alternative hypothesis in the TI-84 LinReg t-test menu?
    Because it determines whether you are testing for any correlation, positive correlation, or negative correlation.
  • What does a strong positive r value (e.g., r ≈ 0.99) suggest about the variables?
    It suggests a strong positive linear correlation between the variables in the sample.
  • What is the purpose of comparing the p-value to the alpha level in hypothesis testing?
    To decide whether to reject or fail to reject the null hypothesis.
  • Does this hypothesis test determine the exact value of the population correlation coefficient ρ?
    No, it only tests whether there is evidence for a nonzero linear correlation, not the exact value of ρ.
  • What does the test establish if you reject the null hypothesis for ρ?
    It establishes that there is a statistically significant linear correlation between the two variables.
  • Why is it important to read the problem text carefully when setting up your hypotheses?
    Because the wording determines whether you test for any correlation, positive correlation, or negative correlation.