Question

The following hypotheses are given. He:p20 Hip<0 A random sample of 15 paired observations has a correlation of - 46. Can we conclude that the correlation in the population is less than zero? Use the 05 significance level. 1. State the decision rule for 0.05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Reject HO ift 2. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic is 3. Can we conclude that the correlation in the population is less than zero? Use the 0.05 significance level. HO. We conclude that the correlation in the population is zero

Answer 1

Q1) For n - 2 = 13 degrees of freedom and 0.05 level of significance, as this is a one tailed test, we have from t distribution tables here:

P( t₁₃ < -1.771) = 0.05

Therefore the decision rule here is given as

Reject H0 if t < -1.771

Q2) The test statistic here is computed as:

$t^*= \frac{r\sqrt{n-2}}{\sqrt{1 - r^2}} = \frac{- 0.46*\sqrt{13}}{\sqrt{1 - 0.46^2}} = -1.868$

therefore - 1.868 is the test statistic value here.

Q3) As the test statistic value here is -1.868 < -1.771, therefore it lies in the rejection region here. Therefore we can Reject H0 here. We have sufficient evidence here to conclude that the correlation in the population is less than 0.