Question

In this problem, we use your critical values table to explore the significance of r based on different sample sizes.

(a) Is a sample correlation coefficient ρ = 0.81 significant at the α = 0.01 level based on a sample size of n = 3 data pairs? What about n = 13 data pairs? (Select all that apply.)

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 3 and α = 0.01.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 3 and α = 0.01.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 3 and α = 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 = 13 and α = 0.01.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 13 and α = 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 = 13 and α = 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 = 3 and α = 0.01.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 13 and α = 0.01.

(b) Is a sample correlation coefficient ρ = 0.40 significant at the α = 0.05 level based on a sample size of n = 20 data pairs? What about n = 30 data pairs? (Select all that apply.)

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 20 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 30 and α = 0.05.

No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 20 and α = 0.05.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 20 and α = 0.05.

No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 30 and α = 0.05.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 30 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 30 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 20 and α = 0.05.

Answer 1

a)

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 3 and α = 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 = 13 and α = 0.01.

b)

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 20 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 30 and α = 0.05.