Question 774927
Question:
The following hypotheses are given.
{{{H[0]}}}:p ≤ 0
{{{H[1]}}}):p > 0
A random sample of 15 paired observations have a correlation of -.46. Can we
conclude that the correlation in the population is less than zero? Use the.05
significance (Lind. Statistical Techniques in Business & Economics. 2012)
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Answer:
The hypotheses should be
{{{H[0]}}}:p ≥ 0
{{{H[1]}}}:p < 0
&#945; = .05
Test Statistic: t, df = 13
Critical Value: -1.7709
t = {{{r*sqrt((n-2)/(1-r^2))}}}  = {{{-0.46*sqrt((15-2)/(1-(-0.46)^2))}}} = -1.8679
P-Value: 0.0422
Reject {{{H[0]}}} because the p-value is less than &#945; = .05. Sample provides evidence to support the claim that the correlation in the population is less than zero.