The Airline Passenger Association studied the relationship b

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 29 flights, the correlation between the number of passengers and total fuel cost was 0.675.

State the decision rule for 0.025 significance level: H₀: 0; H₁: > 0 (Round your answer to 3 decimal places.)

Can we conclude that the correlation in the population is greater than zero? Use the 0.025 significance level

Solution

Set Up Hypothesis
Nuull,H0: <= 0
Alternative, H1: >0
Test Statistic
Value of ( r ) =0.675
Number (n)=29
we use Test Statistic (t) = r / Sqrt(1-r^2/(n-2))
to=0.675/(Sqrt( ( 1-0.675^2 )/(29-2) )
to =4.75
|to | =4.75
Critical Value
The Value of |t | at LOS 0.025% is 2.052
We got |to| =4.75 & | t | =2.052
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho

1. Reject H0 if t > 2.052
2. to =4.75
3. Reject Ho, It is reasonable to conclude that there is positive association in the
population between the two variables.