Question

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Test whether or not the population correlation coefficient (rho) differs from zero. Use alpha = 0.05

Answer 1

Solution:

Here, we have to use t test for the population correlation.

H0: ρ = 0 versus Ha: ρ ≠ 0

This is a two tailed test.

α = 0.05

n = 12

df = n – 2 = 10

r = 0.949383

Test statistic formula is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

t = 0.949383*sqrt(12 - 2)/sqrt(1 - 0.949383^2)

t = 9.557471

P-value = 0.0000

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the population correlation coefficient differs from zero.