Question

(a) Suppose n = 6 and the sample correlation coefficient is r=0.894. IS significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) critical Conclusion: Yes, the correlation coefficient p is significantly different from 0 at the 0.01 level of significance. No, the correlation coefficient p is not significantly different from 0 at the 0.01 level of significance. (b) Suppose n = 10 and the sample correlation coefficient is r = 0.894. Isr significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) critical Conclusion: Yes, the correlation coefficient p is significantly different from o at the 0.01 level of significance. No, the correlation coefficient p is not significantly different from 0 at the 0.01 level of significance. (c) Explain why the test results of parts (a) and (b) are different even though the sample correlation coefficient r = 0.894 is the same in both parts. Does it appear that sample size plays an important role in determining the significance of a correlation coefficient? Explain. As n decreases, the degrees of freedom and the test statistic increase. This produces a smaller P value. As n increases, so do the degrees of freedom, and the test statistic. This produces a smaller P value. As n increases, the degrees of freedom and the test statistic decrease. This produces a smaller P value. As n increases, so do the degrees of freedom, and the test statistic. This produces a larger P value.

Answer 1

@ 1- "-2 = 0.89416-2 Ti-va T-0.8942 = 3.99047 = 3.990 df = 6-2= 4,2= 0.01 ** Critical t = 4,60224 ~ 4.602 ** No, the correlation coefficient p is not significantly different from o at the 0.01 level of significance @t--- 0.894/10-2 5-r2 TT-0.8942 = 5.64338 25.643 df-10-2= 8, X=0.01 ** Critical t = 3.35536 |3.355 ** Yes, the correlation coefficient pis significantly different from o at the 0.01 level of significance. © As n increases, so do the degrees of freedom, and the test statistic. This produce a smaller P value.