webassign.net/web/Student/Assignment-Responses/submit?dep=33426111\&tags=autosave\#question3780148_4 Classes Sis \( k-12360 \) Launch In this problem, we use your critical values table to explore the significance of \( r \) based on different sample sizes. Crtical Vatues for Correlaton Coelildent \( p \) \begin{tabular}{rcc|ccc|ccc} \hline\( n \) & \( \alpha=0.05 \) & \( \alpha=0.01 \) & \( n \) & \( \alpha=0.05 \) & \( \alpha=0.01 \) & \( n \) & \( \alpha=0.05 \) & \( \alpha=0.01 \) \\ \hline 3 & 1.00 & 1.00 & 13 & 0.53 & 0.68 & 23 & 0.41 & 0.53 \\ 4 & 0.95 & 0.99 & 14 & 0.53 & 0.66 & 24 & 0.40 & 0.52 \\ 5 & 0.88 & 0.96 & 15 & 0.51 & 0.64 & 25 & 0.40 & 0.51 \\ 6 & 0.81 & 0.92 & 16 & 0.50 & 0.61 & 26 & 0.39 & 0.50 \\ 7 & 0.75 & 0.87 & 17 & 0.48 & 0.61 & 27 & 0.38 & 0.49 \\ 8 & 0.71 & 0.83 & 18 & 0.47 & 0.59 & 28 & 0.37 & 0.48 \\ 9 & 0.67 & 0.80 & 19 & 0.46 & 0.58 & 29 & 0.37 & 0.47 \\ 10 & 0.63 & 0.76 & 20 & 0.44 & 0.56 & 30 & 0.36 & 0.46 \\ 11 & 0.60 & 0.73 & 21 & 0.43 & 0.55 & & & \\ 12 & 0.58 & 0.71 & 22 & 0.42 & 0.54 & & & \\ \hline \end{tabular} (a) Is a sample correlation coefficient \( \rho=0.83 \) significant at the \( \alpha=0.01 \) level based on a sample size of \( n=5 \) data pairs? What about \( n=9 \) data pairs? (Select all that apply.) No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of \( n=5 \) and \( \alpha=0.01 \). Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of \( n=5 \) and \( \alpha=0.01 \). Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of \( n=9 \) and \( \alpha=0.01 \). No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of \( n=9 \) and \( \alpha=0.01 \). Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of \( n=5 \) and \( \alpha=0.01 \). Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of \( n=9 \) and \( \alpha=0.01 \). No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of \( n=9 \) and \( \alpha=0.01 \).
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The question asks whether a sample correlation coefficient \( r = 0.83 \) is significant at the \( \alpha = 0.01 \) level for different sample sizes, specifically \( n = 5 \) and \( n = 9 \). We need to compare \( r \) with the critical values provided in the Show more…
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