Question

(a) Suppose n = 6 and the sample correlation coefficient is r = 0.882. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.)

t	=
critical t	=

Conclusion:

Yes, the correlation coefficient ρ is significantly different from 0 at the 0.01 level of significance.

No, the correlation coefficient ρ is not significantly different from 0 at the 0.01 level of significance.     

(b) Suppose n = 10 and the sample correlation coefficient is r = 0.882. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.)

t	=
critical t	=

Conclusion:

Yes, the correlation coefficient ρ is significantly different from 0 at the 0.01 level of significance.

No, the correlation coefficient ρ is not significantly different from 0 at the 0.01 level of significance.     

(c) Explain why the test results of parts (a) and (b) are different even though the sample correlation coefficient r = 0.882 is the same in both parts. Does it appear that sample size plays an important role in determining the significance of a correlation coefficient? Explain.

As n increases, the degrees of freedom and the test statistic decrease. This produces a smaller P value.

As n increases, so do the degrees of freedom, and the test statistic. This produces a smaller P value.

As n increases, so do the degrees of freedom, and the test statistic. This produces a larger P value.

As n decreases, the degrees of freedom and the test statistic increase. This produces a smaller P value.

Answer 1