Problema Solution
A data set of size 19 has correlation coefficient of r = –0.432. Test the significance of r at the 5% level and at the 1% level.
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TEST STATISTIC FOR CORRELATION COEFFICIENT r, t-DISTRIBUTION, SMALL SAMPLE
TEST STATISTIC t = [r * sqrt(n - 2)] / sqrt(1 - r^2)
r = CORRELATION COEFFICIENT [-0.432]
n = SAMPLE SIZE [19]
t = -1.63513
Table P-value for two-tailed test based on n - 1 = 18 df is (approx.) 0.11 That is; at either significance level of 5% (0.05)and at 1% (0.01) there is clear evidence the Correlation Cofficient [linear relationship] is significant.
r is significant at 5% and at 1%