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 = 0.86 significant at the α = 0.01 level based on a sample size of n = 5 data pairs? What about n = 14 data pairs? (Select all that apply.)

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.

No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 14 and α = 0.01.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 14 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 = 14 and α = 0.01.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 14 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.

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.

(b) Is a sample correlation coefficient ρ = 0.42 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.

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.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 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 = 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.

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.

Answer 1

Solution-A;

r=0.86

n=5

df=n-2=3

for alpha=0.01 and df=3 critical r value is

r crit=0.959

r < r crit

Fail to reject Ho

for n=18

df=18-2=16

critical r value=0.590

r>rcit

Reject Ho

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 = 14 and α = 0.01.

Solution-B:

r=0.42

for n=20

df=n-2=20-2=18

critical r =0.444

0.42<0.444

fail to reject Ho

No relationship exists

for n=30

df=n-2=30-2=28

r critical=0.381

0.42>0.381

Reject Ho

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.