## Exploring the Significance of Correlation Coefficients based on Different Sample SizesIn this problem, we use critical values to explore the significance of the correlation coefficient \( r \) based on different sample sizes.### Critical Values for Correlation Coefficient \( r \)\[\begin{array}{|c|c c|c c|}\hlinen & \alpha = 0.05 & \alpha = 0.01 & \alpha = 0.05 & \alpha = 0.01 \\\hline3 & 1.000 & 1.000 & - & - \\4 & 0.950 & 0.990 & - & - \\5 & 0.878 & 0.950 & - & - \\6 & 0.811 & 0.917 & - & - \\7 & 0.754 & 0.875 & - & - \\8 & 0.707 & 0.834 & - & - \\9 & 0.666 & 0.798 & - & - \\10 & 0.632 & 0.765 & - & - \\11 & 0.602 & 0.735 & - & - \\12 & 0.576 & 0.707 & - & - \\13 & 0.552 & 0.681 & - & - \\14 & 0.532 & 0.657 & - & - \\15 & 0.514 & 0.634 & - & - \\16 & 0.497 & 0.612 & - & - \\17 & 0.482 & 0.592 & - & - \\18 & 0.468 & 0.574 & - & - \\19 & 0.456 & 0.556 & - & - \\20 & 0.444 & 0.540 & - & - \\21 & 0.433 & 0.524 & - & - \\22 & 0.423 & 0.509 & - & - \\23 & 0.413 & 0.495 & - & - \\24 & 0.404 & 0.482 & - & - \\25 & 0.396 & 0.469 &

(a) Condition: If | ρ | ≥ absolute value then r is said to be significant and there is sufficient…

(a) Is a sample correlation coefficient p = 0.86 significant at the a = 0.01 level based on a sample size of n = 4 data pairs? What about n = 12 data pairs? (Select all that apply.) O No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 4 and a = 0.01. O Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size ofn = 4 and a = 0.01. O Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 12 and a = 0.01. O No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 12 and a = 0.01. O Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 4 and a = 0.01. O No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 12 and a = 0.01. O Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size ofn = 12 and a = 0.01. O No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 4 and a = 0.01. (b) Is a sample correlation coefficient p = 0.43 significant at the a = 0.05 level based on a sample size of n = 18 data pairs? What about n = 29 data pairs? (Select all that apply.) O No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 18 and a = 0.05. O Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size ofn = 18 and a = 0.05. O Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 and a = 0.05. O No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 and a = 0.05. O Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 29 and a = 0.05. O Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 29 and a = 0.05. O No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n 29 and a = 0.05. O No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 29 and a = 0.05. (c) Is it true that in order to be significant, ap value must be larger than 0.90? larger than 0.70? larger than 0.50? What does sample size have to do with the significance of p? Explain your answer. o Yes, a larger correlation coefficient of 0.70 means that the data will be significant. o No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant. o No, sample size has no bearing on whether or not the correlation coefficient might be significant. o Yes, a larger correlation coefficient of 0.90 means that the data will be significant. o Yes, a larger correlation coefficient of 0.50 means that the data will be significant.