Question

Consider the following competing hypotheses:

H0: ρxy = 0
HA: ρxy ≠ 0

The sample consists of 27 observations and the sample correlation coefficient is 0.38. [You may find it useful to reference the t table.]

a-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

TEST STATISTIC: ________

a-2. Find the p-value.

0.02 p-value < 0.05
0.01 p-value < 0.02
p-value < 0.01
p-value 0.10
0.05 p-value < 0.10

b. At the 1% significance level, 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)

Test statistic is given by:

TEST STATISTIC:   2.054

(a - 2)

ndf = n - 2 = 27 - 2 = 25

By Technology, p - value = 0.0506

So,

Correct option:

0.05 < p - value < 0.10

(b)

Correct option:

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