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 0.025 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.)

Answer 1

Solution:
Sample size = n = 20

the correlation between the number of passengers and total fuel cost was 0.688.

r = 0.688

Part 1) State the decision rule for 0.025 significance level: H₀: ρ ≤ 0; H₁: ρ > 0.

For testing correlation coefficient, we use:

df = n - 2 = 20 - 2 = 18

significance level = 0.025

H1 is > type , thus this is right tailed ( one tailed test)

Thus look in t table for df = 18 and one tail area = 0.025 and find t critical value

t critical value = 2.101

Thus the decision rule is:

Reject null hypothesis H0, if t test statistic value > t critical value = 2.101

Part 2) Compute the value of the test statistic.

Since t test statistic value = 4.02 > t critical value = 2.101 , we reject H0.