Question

The Airline Passenger Association studied the relationship between the number of passengers on a particular flight and the cost of the flight. It seems logical that more passengers on the flight will result in more weight and more luggage, which in turn will result in higher fuel costs. For a sample of 20 flights, the correlation between the number of passengers and total fuel cost was 0.688.

(1)	State the decision rule for 0.02 significance level: H0: ρ ≤ 0; H1: ρ > 0 (Round your answer to 3 decimal places.)

Reject H0 if t >

(2)	Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic

(3)	Can we conclude that the correlation in the population is greater than zero? Use the 0.02 significance level

(Click to select)Do not rejectReject H0 . It is (Click to select)reasonablenot reasonable to conclude that there is positive association in the   population between the two variables.

Answer 1

Solution:

r = 0.688
n = 20
(1) alpha = 0.02
df = n-2 = 18

Ha : ρ > 0
=> on-sided test
t_critical = t(alpha,df) = t(0.02, 18) = 2.214
Reject H0 if t > 2.214

(2) test statistic = r*sqrt( (n-2)/(1-r^2) ) = 0.688*sqrt(18/(1-0.688^2)) = 4.022

(3) Calculated t = 4.022 > 2.214, the table value.

The null hypothesis is rejected.

It is to conclude that there is positive association between the number of passengers on a particular flight and the cost of the flight.