Question

Consider the following competing hypotheses: H0: ρxy = 0 HA: ρxy ≠ 0 The sample consists of 26 observations and the sample correlation coefficient is 0.69. [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.)

a-2. Find the p-value. p-value 0.10 0.05 p-value < 0.10 0.02 p-value < 0.05 0.01 p-value < 0.02 p-value < 0.01

b. At the 5% significance level, what is the conclusion to the test?

Do not reject H0; we cannot 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.

Reject H0; we can state the variables are correlated.

Answer 1

H0: ρxy = 0 HA: ρxy ≠ 0

ρxy repersents the correlation coefficient between x and y

sign in Ha indicates the two tailed test.

n = 26

r = 0.69

Degrees of freedom d.f. = n -2 = 26 -2 = 24

The test statistic is given by

a - 1)

t =   

=   

= 4.670

The value of test statistic t = 4.670

a -2 ) t = 4.670 , d.f. = 24 , Two tailed test

So , p value = 0.000096

p value < 0.01

b)At the 5% significance level, what is the conclusion to the test?

p value is less than 5% significance level.

Reject H0; we can state the variables are correlated.