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Inferences for Slope quiz

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  • What does the null hypothesis state about the slope (β) in regression analysis?
    The null hypothesis states that β equals zero, indicating no linear correlation between the variables.
  • What is the alternative hypothesis when testing for any linear correlation between two variables?
    The alternative hypothesis is that β is not equal to zero, suggesting a linear relationship exists.
  • Which TI-84 function is used to perform a hypothesis test for the slope (β)?
    The LinRegTTest function is used to perform a hypothesis test for β on the TI-84 calculator.
  • What does a p-value less than alpha (α=0.05) indicate in a hypothesis test for β?
    A p-value less than alpha means we reject the null hypothesis and conclude there is significant linear correlation.
  • How do you enter data for a regression test on the TI-84 calculator?
    Enter the x-variable data in L1 and the y-variable data in L2 using the STAT and ENTER buttons.
  • What should the frequency be set to when running LinRegTTest or LinRegTInt on the TI-84?
    The frequency should be set to 1, which is the default setting.
  • What is the purpose of constructing a confidence interval for β?
    A confidence interval for β estimates the range in which the true slope likely falls and assesses linear correlation.
  • Which TI-84 function is used to calculate a confidence interval for the slope (β)?
    The LinRegTInt function is used to calculate a confidence interval for β on the TI-84.
  • What does it mean if a 95% confidence interval for β does not include zero?
    It means we are 95% confident that the slope is not zero, indicating significant linear correlation.
  • How do you select the correct alternative hypothesis in LinRegTTest on the TI-84?
    Choose the option that matches the problem, such as β ≠ 0 for testing any linear correlation.
  • What is the interpretation if the confidence interval for β includes zero?
    If the interval includes zero, there is not enough evidence to conclude a significant linear relationship.
  • What is the significance of the slope (β) in a regression line?
    The slope indicates the strength and direction of the linear relationship between two variables.
  • What is the default confidence level used in most regression confidence interval problems?
    The default confidence level is 95%, or 0.95.
  • What does rejecting the null hypothesis in a slope test imply about the variables?
    Rejecting the null implies there is enough evidence to suggest a linear correlation between the variables.
  • How do you interpret a p-value of 3.4 x 10^-6 in a slope hypothesis test with α=0.05?
    Since the p-value is much less than α, we reject the null hypothesis and conclude a significant linear relationship exists.