Considering the following one-dimensional data points for clustering using Euclidean distance.

x1= 1, x2 = 5, x3 =5, x4 = 8, x5 = 9, x6 = 9, x7 = 10, x8=12

Using a clustering algorithm, x1 and x2 are put in one cluster; x3, x4 and x5 are put in another cluster; and x6, x7 and x8 are put in another cluster.

1. Compute pseudo-F statistic for this clustering. At a significance level of 0.05, find whether the test outcome suggests the existence of these three clusters.

Compute silhouette score.