Assignment:
From 1789 through 1870, the last names of associate justices appointed to the U.S. Supreme Court were as coded below. Last names beginning with A–M are shown as a “1,” those beginning with N–Z as a “2.” Compare the observed number of runs with the expected number, then interpret what this difference might mean in terms of the sequence of the appointees. At the 0.10 level of significance, test the randomness of this series.
221111212111212221
121111221111211121
Provide complete and step by step solution for the question and show calculations and use formulas.