A sample of 30 observations provides the following statistics: sx = 14; sy = 19; sxy = -150.a. Calculate and interpret the sample correlation coefficient rxy.b. Specify the hypotheses to determine whether or not x and y are significantly correlated.c. At the 5% significance level, what is the conclusion to the test using the critical-value approach? Explain.d. At the 5% significance level, what is the conclusion to the test using the p-value approach? Explain.
What will be an ideal response?
a. rxy = -0.56; moderate negative linear relationship.
b. H0: ?xy = 0; HA: ?xy ? 0.
c. t28 = -3.58; Reject H0 if t28 < -2.048 or t28 > 2.048. Reject the null hypothesis; we can conclude the variables are correlated.
d. Using the t-table, the p-value < 0.005; Since the p-value < ? = 0.05, reject H0; We can conclude the variables are correlated.
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