Use the following results obtained from a simple linear regression analysis with 12 observations.
= 37.2895 − (1.2024)X
r2 = .6744sb = .2934
Test to determine if there is a significant negative relationship between the independent and dependent variables at α = .05. Give the test statistic and the resulting conclusion.
The following needs to be tested:
where \rhoρ corresponds to the population correlation.
The sample size is n = 12 so then the number of degrees of freedom is df = n-2 = 12 - 2 = 10
The corresponding t-statistic to test for the significance of the correlation is:
The p-value is computed as follows:
Since we have that p = 0.9919 ≥0.05, it is concluded that the null hypothesis H0 is not rejected.
Therefore, based on the sample correlation provided, it is concluded that there is not enough evidence to claim that the population correlation ρ is less than 0, at the 0.05 significance level.
Get Answers For Free
Most questions answered within 1 hours.