We are examining the relationship between the number of cold calls a broker makes and the number of accounts the firm as a whole opens. We have determined that the correlation coefficient is equal to 0.70, based on a sample of 16 observations. Is the relationship statistically significant at a 10 percent level of significance, and why or why not? The relationship is: A) significant; the t-statistic exceeds the critical value by 1.91. B) not significant; the critical value exceeds the t-statistic by 1.91. C) significant; the t-statistic exceeds the critical value by 3.67. D) not significant; the critical value exceeds the t-statistic by 4.21.
Correct answer is: A) significant; the t-statistic exceeds the critical value by 1.91 t = ((16-2)^1/2*0.7)/((1-0.7^2)^1/2) = 3.69 t(critical) = 1.761 for alpha = 0.1 and df = 14 (two tailed test) t - t(critical) = 1.92 (small difference might be the result of rounding)