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: Hop: 0; Hi:p<0 (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Reject Ho ift< Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Value of the test statistic Can we conclude that there is a negative association between the two variables? Use the 0.05 significance level. Ho. There is evidence to conclude that there is a negative association in the population between the mean number of square feet per office worker and the mean monthly rental rate in the central business district.

Answer 1

Decision rule

Reject null hypothesis if t < -t(α, n - 2 )
t(α, n-2) = t(0.05 , 40 - 2 ) = 1.686
t < - 1.686

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( -0.363 * √(40 - 2) ) / (√(1 - 0.1318) )
t = -2.40

Reject null hypothesis if t < -t(α, n - 2 )
t(α, n-2) = t(0.05 , 40 - 2 ) = 1.686
t < -t(α,n-2) = -2.4015 < -1.686
Result :- Reject null hypothesis

Ho. There is evidence to conclude that there is a negative association in the population between the mean number of square feet per office worker and the mean monthly rental rate in the central business district.

Reject H0, There is sufficient evidence