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 = 5 data pairs? What about n = 9 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 = 9 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 = 5 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 = 5 and α = 0.01.

[ ] No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 5 and α = 0.01.

[ ] Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 5 and α = 0.01.

[ ] Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 9 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 = 9 and α = 0.01.

[ ] No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 9 and α = 0.01.

(b) Is a sample correlation coefficient ρ = 0.42 significant at the α = 0.05 level based on a sample size of n = 18 data pairs? What about n = 28 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 = 28 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 = 28 and α = 0.05.

[ ] No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 28 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 = 18 and α = 0.05.

[ ] Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 and α = 0.05.

[ ] No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 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 = 28 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 = 18 and α = 0.05.

(c) Is it true that in order to be significant, a ρ 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 ρ? Explain your answer.

[ ] Yes, a larger correlation coefficient of 0.90 means that the data will be significant.

[ ] Yes, a larger correlation coefficient of 0.50 means that the data will be significant.   

[ ] No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant.

[ ] No, sample size has no bearing on whether or not the correlation coefficient might be significant.

[ ] Yes, a larger correlation coefficient of 0.70 means that the data will be significant.

Answer 1

Solution

(a) Is a sample correlation coefficient ρ = 0.81 significant at the α = 0.01 level based on a sample size of n = 5 data pairs? What about n = 9 data pairs?

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 5 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 = 9 and α = 0.01.

(b) Is a sample correlation coefficient ρ = 0.42 significant at the α = 0.05 level based on a sample size of n = 18 data pairs? What about n = 28 data pairs?

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 18 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 = 28 and α = 0.05.

(c) Is it true that in order to be significant, a ρ 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 ρ?

Yes, a larger correlation coefficient of 0.90 means that the data will be significant.

Yes, a larger correlation coefficient of 0.50 means that the data will be significant.   

Yes, a larger correlation coefficient of 0.70 means that the data will be significant.