Question

(a) Suppose n = 6 and the sample correlation coefficient is r = 0.888. 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 ? is significantly different from 0 at the 0.01 level of significance.

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

(b) Suppose n = 10 and the sample correlation coefficient is r = 0.888. 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 ? is significantly different from 0 at the 0.01 level of significance.

No, the correlation coefficient ? 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 = 0.888 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 decreases, the degrees of freedom and the test statistic increase. This produces a smaller P value.

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 larger P value.

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

Answer 1

vs

Decision rule : P value < 0.1  then reject

(a) We have given, n = 6 and the sample correlation coefficient is r = 0.888.

Degree of freedom =n-2 = 6 - 2 = 4

=3.862

t critical value at the 0.01 level of significance with degree of freedom 4 is 0.917

P value is 0.018 > 0.01 therefore, we fail to reject H0.

P value by using =TDIST(3.862,4,2)

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

(b) Here we have, n = 10 and the sample correlation coefficient is r = 0.888.

=5.462

t critical value at the 0.01 level of significance with degree of freedom 8 is 0.765

P value is 0.0006 < 0.01 therefore, we reject H0.

P value by using =TDIST(5.462,8,2)

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

(c)

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