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Inferences for the Correlation Coefficient - Excel quiz

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  • What does the sample correlation coefficient r indicate about the relationship between two variables?
    If r is close to zero, there is weak or no linear correlation; if r is far from zero, there is strong linear correlation.
  • What is the null hypothesis when testing for the population correlation coefficient ρ?
    The null hypothesis is that ρ equals zero, indicating no linear correlation between the variables.
  • How do you determine the sign for the alternative hypothesis in a correlation test?
    The sign depends on the claim: use '>' for positive correlation, '<' for negative, and '≠' if testing for any linear correlation.
  • What is the formula for degrees of freedom in a correlation coefficient hypothesis test?
    Degrees of freedom is calculated as n - 2, where n is the sample size.
  • Which Excel function is used to calculate the sample correlation coefficient r?
    The function is =CORREL(x_data, y_data).
  • What is the formula for the t statistic in a correlation coefficient hypothesis test?
    The t statistic is t = r / sqrt((1 - r^2) / (n - 2)).
  • How do you calculate the p-value for a two-tailed correlation test in Excel?
    Use the function =T.DIST.2T(t_score, degrees_of_freedom).
  • What does a p-value less than alpha (α) indicate in a correlation coefficient hypothesis test?
    It means you reject the null hypothesis and conclude there is significant linear correlation.
  • If the p-value is greater than alpha, what is the conclusion regarding the null hypothesis?
    You fail to reject the null hypothesis, indicating insufficient evidence for linear correlation.
  • What is the sample size in the example provided for testing correlation in Excel?
    The sample size is 13.
  • What was the calculated sample correlation coefficient r in the example?
    The calculated r was approximately 0.74.
  • What was the calculated t score in the example for the correlation test?
    The t score was about 3.68.
  • What was the calculated p-value in the example, and how did it compare to alpha?
    The p-value was about 0.004, which is less than the alpha of 0.05.
  • What conclusion was reached in the example after comparing the p-value to alpha?
    The null hypothesis was rejected, indicating significant linear correlation between playtime and enjoyment score.
  • What is the purpose of hypothesis testing for the population correlation coefficient ρ?
    It evaluates whether a linear relationship observed in sample data is significant enough to extend to the population.