Question

Consider the following competing hypotheses:

H₀: ρ_xy ≥ 0
H_A: ρ_xy < 0

The sample consists of 30 observations and the sample correlation coefficient is –0.46. [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 < 0.01

• p-value

  

  0.10
• 0.05

  

  p-value < 0.10
• 0.025

  

  p-value < 0.05
• 0.01

  

  p-value < 0.025

b. At the 5% significance level, what is the conclusion to the test? conclude that the population correlation coefficient between x and y is less than zero. HO, we

Answer 1

Test Statistic :-
$t = (r * \sqrt{n - 2}) / (\sqrt{1 - r^2})$

t = -2.741

t = (-0.46 * V30-2)バV1-0.2116)

Test Criteria :-
Reject null hypothesis if
t <-to


t0.05.30-2-1.7011 ta,n-2


t < _ta.n-2-一2.741 <ー1.70 11

Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 2.741 ) = 0.0053
Reject null hypothesis if P value < level of significance
P - value = 0.005 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

a-0.05

• p-value < 0.01

conclude that the population correlation coefficient between x and y is less than zero. Ho, we

Reject H0, There is sufficient evidence to conclude