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Inferences for the Correlation Coefficient - Excel quiz

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  • What does the correlation coefficient r tell us about two variables?
    It tells us the strength and direction of the linear relationship 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 symbol is used in the alternative hypothesis if we are testing for any linear correlation (not just positive or negative)?
    We use the not equal to symbol (≠) in the alternative hypothesis.
  • How do you calculate the degrees of freedom for the correlation coefficient hypothesis test?
    Degrees of freedom are calculated as the sample size n minus 2.
  • Which Excel function is used to calculate the sample correlation coefficient r?
    The function is =CORREL(array1, array2).
  • What is the formula for the t statistic in testing the population correlation coefficient?
    The formula is t = r * sqrt((n-2)/(1-r^2)).
  • Which Excel function is used to calculate the two-tailed p-value from the t statistic?
    The function is =T.DIST.2T(t, degrees_freedom).
  • What does a p-value less than the alpha level indicate in this hypothesis test?
    It indicates that we reject the null hypothesis and conclude there is significant linear correlation.
  • If the sample correlation coefficient r is close to zero, what does this suggest?
    It suggests there is weak or no linear correlation between the variables.
  • What is the typical alpha level used in hypothesis testing for correlation?
    A common alpha level is 0.05.
  • What does it mean if we reject the null hypothesis in a correlation test?
    It means there is enough evidence to conclude that a linear correlation exists between the variables.
  • In the example, what was the sample size and the resulting degrees of freedom?
    The sample size was 13, so the degrees of freedom were 11.
  • What was the approximate value of r in the example provided?
    The value of r was approximately 0.74.
  • What was the calculated t score in the example?
    The t score was about 3.68.
  • What was the p-value in the example, and what conclusion was drawn?
    The p-value was about 0.004, which led to rejecting the null hypothesis and concluding a significant linear correlation.