Example 16.1

EXAMPLE 16.1 Perform the Significance Test

CASE 16.1 In Case 16.1, $n_{1} = 12$ , $n_{2} = 8$ , and there are $N = 20$ observations in all. The sum of ranks for the 12 Used Auto consumers has mean

$\begin{array}{l} μ_{W} & = & \frac{n_{1} (N + 1)}{2} \\ = & \frac{(12) (21)}{2} = 126 \end{array}$

and standard deviation

$\begin{array}{l} σ_{W} & = & \sqrt{\frac{n_{1} n_{2} (N + 1)}{12}} \\ = & \sqrt{\frac{(12) (8) (21)}{12}} = \sqrt{168} = 12.961 \end{array}$

The observed sum of the ranks, $W = 155$ , is higher than the mean by a bit more than two standard deviations since $(155 - 126) / 12.961 = 2.24$ . It appears that the data support the suspicion that Used Auto consumers are being discriminated against regarding price. The $P$ -value for our one-sided alternative is $P (W \geq 155)$ , the probability that $W$ is at least as large as the value for our data when $H_{0}$ is true.