SOLUTION: The following hypotheses are given. H0(small zero):p < or equal to 0 H1 (small one):p > 0 A random sample of 15 paired observations have a correlation of -.46. Can we conc

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Question 774927: The following hypotheses are given.
H0(small zero):p < or equal to 0
H1 (small one):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)
Answer by reviewermath(1029) About Me  (Show Source):
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Question:
The following hypotheses are given.
H%5B0%5D:p ≤ 0
H%5B1%5D):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%5B0%5D:p ≥ 0
H%5B1%5D:p < 0
α = .05
Test Statistic: t, df = 13
Critical Value: -1.7709
t = r%2Asqrt%28%28n-2%29%2F%281-r%5E2%29%29 = -0.46%2Asqrt%28%2815-2%29%2F%281-%28-0.46%29%5E2%29%29 = -1.8679
P-Value: 0.0422
Reject H%5B0%5D because the p-value is less than α = .05. Sample provides evidence to support the claim that the correlation in the population is less than zero.