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 8 flights, the correlation between the number of passengers and total fuel cost was 0.634.
1. State the decision rule for 0.01 significance level: H0: ? ? 0; H1: ? > 02) Compute the value of the test statistic

Answer 1

Answer:

1) Reject null hypothesis if t > 3.143

2) t = 2.008

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 8

Correlation, r = 0.634

Significance level = 0.01

First we design the null and the alternate hypothesis:

$H_{0}: \rho \leq 0\\H_A: \rho > 0$

This is a one tailed test.

1) Decision rule

Degree of freedom  = n - 2 = 6

$t_{critical} \text{ at 0.01 level of significance, 6 degree of freedom } = 3.143$

So if the calculated test statistic is greater than 3.143, we fail to accept the null hypothesis and reject it.

2) Test statistic

$t_{stat} = \dfrac{r\sqrt{n-2}}{\sqrt{1-r^2}}\\\\t_{stat} = \dfrac{(0.634)\sqrt{8-2}}{\sqrt{1-(0.634)^2}}\\\\t_{stat} = 2.008$