Question

1. A golf course grounds keeper wants to know if there's a positive linear relationship between the density of seed and the density of new grass 6 months later. Does the following data justify concluding there is a positive linear relationship at a = 5%? Seed Density Grass Density 1 170 2 200 3 240 4 300 5 310 6 290 7 290

Answer 1

Correlation: r (Using Excel function CORREL(x,y)) = 0.861

n = 7, Degrees of freedom: df = n-2 = 5

Level of significance = 0.05

H₀: ρ = 0, There is no positive linear relationship between seed density and grass density

H₁: ρ > 0, There is a positive linear relationship between seed density and grass density

Test statistic: t = r*((1-r*r)/(n-2))^0.5 = 0.861*((1-0.861*0.861)/(7-2))^0.5 = 0.196

Critical value (Using Excel function ABS(T.INV(probability,df))) = ABS(T.INV(0.05,5)) = 2.015

Since test statistic is less than critical value, we do not reject the null hypothesis.

So, there is no positive linear relationship between seed density and grass density.