Question

Consider the following competing hypotheses:

H0: ρxy = 0

HA: ρxy ≠ 0

The sample consists of 25 observations and the sample correlation coefficient is 0.15. Use Table 2.

a-1.	At the 5% significance level, specify the critical value(s). (Round your answer to 3 decimal places.)

Critical value

±

a-2.	Specify the decision rule.
	We reject H0 if t23 < 1.714 or t23 > −1.714. We reject H0 if t23 < 2.069 or t23 > −2.069. We reject H0 if t23 > 1.714 or t23 < −1.714. We reject H0 if t23 > 2.069 or t23 < −2.069.

b.	Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Test statistic

c.	What is the conclusion to the test?
	Reject H0; we can state the variables are correlated. Reject H0; we cannot state the variables are correlated. Do not reject H0; we can state the variables are correlated. Do not reject H0; we cannot state the variables are correlated.

Answer 1

a-1.

Critical value =

a-2.

Decision rule :

We reject H₀ if t₂₃ > 2.069 or t₂₃ < −2.069

b.

Test statistic = 0.74

c.

Conclusion to the test :

Do not reject H₀; we cannot state the variables are correlated