Consider the following competing hypotheses Ho xy 0 HA xy 0

Consider the following competing hypotheses:

Ho: xy = 0

HA: xy 0

The sample consists of 16 observations and the sample correlation coefficient is 0.27.

a.   Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

b-1. At the 5% significance level, specify the critical value(s). (Round your answer to 3 decimal places.)

b-2. Specify the decision rule.

            A. We reject Ho if t14 > 2.145 or t14 < -2.145

            B. We reject Ho if t14 > 1.761 or t14 < -1.761

            C. We reject Ho if t14 < 2.145 or t14 > -2.145

            D. We reject Ho if t14 < 1.761 or t14 > -1.761

c.    What is the conclusion to the test?

             A. Reject Ho; the variables are correlated

            B. Reject Ho; the variables are not correlated

            C. Do not reject Ho; the variables are correlated

            D. Do not reject Ho; the variables are not correlated

Solution

a)

As

t = r sqrt[(n-2)/(1-r^2)]

Then

t = 0.27*sqrt((16-2)/(1-0.27^2)) = 1.049215002

t= 1.05 [ANSWER]

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b-1.

At 5% significance, as df = n - 2 = 14,

tcrit = -2.145, 2.145 [answer]

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b-2.

Thus,

OPTION A: We reject Ho if t14 > 2.145 or t14 < -2.145 [answer]

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c)

As t = 1.05 is not in the rejection region,

OPTION D. Do not reject Ho; the variables are not correlated. [ANSWER]