A research analyst believes that a positive relationship exists between a firm's advertising expenditures and its sales. For 65 firms, she collects data on each firm's yearly advertising expenditures and subsequent sales. She calculates a Spearman rank correlation coefficient of 0.45.
a. Specify the competing hypotheses to determine whether advertising and sales are correlated.
b. Assume that the sampling distribution of rs is approximately normal. Calculate the value of the test statistic and the p-value.
c. At the 5% significance level, are advertising and sales correlated? Explain.