Question

Consider the following competing hypotheses: H0: ρxy = 0 HA: ρxy ≠ 0

The sample consists of 29 observations and the sample correlation coefficient is 0.48. [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 0.10 0.05 p-value < 0.10 0.02 p-value < 0.05 0.01 p-value < 0.02 p-value < 0.01

b. At the 1% significance level, what is the conclusion to the test?

Do not reject H0; we cannot state the variables are correlated.

Reject H0; we cannot state the variables are correlated.

Do not reject H0; we can state the variables are correlated.

Reject H0; we can state the variables are correlated.

Answer 1

The following needs to be tested:

where ρ corresponds to the population correlation.

A1)

A2)

The p value is 0.00840998

p-value < 0.01

b.

Reject H0; we can state the variables are correlated.

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