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. Use Table 2. Click here to find Table 2 or select the table from D2L.

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

Set Up Hypothesis
Under The Null Hypothesis H0: =0
Under The Alternate Hypothesis H1: !=0
Test Statistic
Value of ( r ) =0.27
Number (n)=16
we use Test Statistic (t) = r / Sqrt(1-r^2/(n-2))
to=0.27/(Sqrt( ( 1-0.27^2 )/(16-2) )
to =1.0492
|to | =1.0492
Critical Value
The Value of |t | at LOS 0.05% is 2.145
We got |to| =1.0492 & | t | =2.145
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho

[ANSWER]
to =1.05
Critical Value: The Value of |t | at LOS 0.05% is 2.145
A. We reject Ho if t14 > 2.145 or t14 < -2.145
C. Do not reject Ho; the variables are correlated