Question

A study of 10 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.71.

1. State the decision rule for 0.010 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

   1. Reject H0 if t > _______

2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

3. Can we conclude that the correlation in the population is greater than zero? Use the 0.010 significance level.

Answer 1

Solution:

1)

Given ,

= 0.010

n = 10

r = 0.71

d.f. = n - 2 = 10 - 2 = 8

> sign in H1 indicates that this is RIGHT TAILED TEST.

So , critical value is

(Use t table)

Decision rule is

Reject H0 if t > 2.896

2)

The test statistic is given by

t =

=  

=  2.85

The value of the test statistic t = 2.85

3)

Since 2.85 < 2.896 , test statistic does not fall in rejection region.

So ,

Fail to reject H₀

We cannot conclude that the correlation in the population is greater than zero