Question

For a sample of 40 large U.S. cities, the correlation between the mean number of square feet per office worker and the mean monthly rental rate in the central business district is −0.363.

State the decision rule for .05 significance level: H₀: ρ ≥ 0; H₁: ρ < 0 (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Can we conclude that there is a negative association between the two variables? Use the 0.05 significance level.

Answer 1

Ans:

n=40

df=40-2=38

critical t value=-1.686

Reject H0,if t<-1.686

Test statistic:

t=-0.363*sqrt((40-2)/(1-0.363^2))

t=-2.40

As,t<-1.686,we reject null hypothesis.

There is sufficient evidence to conclude that  there is a negative association between the two variables.