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 9 flights, the correlation between the number of passengers and total fuel cost was 0.734.

1. State the decision rule for 0.010 significance level: H0: rho ≤ 0; H1: rho > 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 0.010 significance level (Click to select)RejectDo not reject H0 . It is (Click to select)not reasonablereasonable to conclude that there is positive association in the population between the two variables.

Answer 1

1)Reject H_o if t> 2.998

2) t = 2.8594

3) No, conclusion about positive association in population is not reasonable

Explanation:

To Test
`H_o : \rho  = 0 vs H_1:\rho>0`

we know that Test statics is

`t = (r√(n-2))/(√(1- r^2)) \sim t_(n-2)`

1) Reject H_o if
`t > t_(n-2)\alpha`

n = 9,
`\alpha = 0.010`

`t_7(0.010) = 2.998`

Reject H_o if t> 2.998

2)
`t = (r√(n-2))/(√(1- r^2))`

n = 9 r = 0.734

so we have t = 2.8594

3) t = 2.8594

therefore
`t < t_7(0.010) = 2.998`, hence we accept hypothesis or H_o

No, conclusion about positive association in population is not reasonable