Question

True or False?

With testing the significance of correlation, a hypothesis test can be used to determine whether the sample correlation coefficient has enough evidence to conclude that the population correlation coefficient is significant.

Answer 1

True

• The symbol for the population correlation coefficient is ρ, the Greek letter rho.
• ρ = population correlation coefficient (unknown).
• r = sample correlation coefficient (known; calculated from sample data).

The hypothesis test lets us decide whether the value of the population correlation coefficient ρ is close to zero or significantly different from zero. We decide this based on the sample correlation coefficient r and the sample size n.

If the test concludes the correlation coefficient is significantly different from zero, we say the correlation coefficient is significant.

• Conclusion: There is sufficient evidence to conclude there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero.
• What the conclusion means: There is a significant linear relationship between x and y. We can use the regression line to model the linear relationship between x and y in the population.