Need Help w/ correlation test assume regression inferences are met. Work answer out

#1
A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the reulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are:

Seed Density, x Lawn Quality, y
1 30
1 40
2 40
3 40
3 50
3 65
4 50
5 50

Using technology, determine whether the data provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated. Test at the 1% significance level using the hypotheses
H not : sigma = 0, H a : sigma > 0.
 
#2
Welcome greatful,

r=0.600 by Minitab.

The test statistic:
T0=r/sqrt[(1-r^2)/(n-2)]
=0.6/sqrt[(1-0.6^2)/(8-2)]
=1.84

At alpha=0.01, df=n-2=6
t(n-2, 1-alpha/2)=t(6, 0.995)=3.707

T0 < 3.707

We do not reject H0.