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 10 flights, the correlation between the number of passengers and total fuel cost was 0.611.

1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

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

3. Can we conclude that the correlation in the population is greater than zero? Use the 0.010 significance level.

   1. ______ H0 it is ________ to conclude that there is + association in the population between the two variables  

Answer 1

Solution:

1)

Given ,

= 0.010

n = 10

r = 0.611

d.f. = n - 2 = 10 - 2 = 8

> sign in H1 indicates that this is RIGHT TAILED TEST.

So , critical value is

(Use t table)

Decision rule is

Reject H0 if t > 2.896

2)

The test statistic is given by

t =

=  

=  2.18

The value of the test statistic t = 2.18

3)

Since 2.18  < 2.896 , test statistic does not fall in rejection region.

So ,

Fail to reject H₀

We cannot conclude that the correlation in the population is greater than zero.

Fail to reject H₀, it is not possible/there is not sufficient evidence to  conclude that there is + association in the population between the two variables