Normal Approximation For each successive presidential term from Franklin Pierce (the 14th president, elected in 1853) to George W. Bush

(43rd president), the party affiliation controlling the White House follow, where R designates Republican and D designates Democrat (Reference: The New York Times Almanac).

Historical Note: We start this sequence with the 14th president because earlier presidents belonged to political parties such as the Federalist or Whig (not Democratic or Republican) party. In cases in which a president died in office or resigned, the period during which the vice president finished the term is not counted as a new term. The one exception is the case in which Lincoln (a Republican) was assassinated and the vice president, Johnson (a Democrat), finished the term.

D D R R D R R R R D R D R R R R D D R R D D D D D R R D D R R D R R R D D R Test the sequence for randomness at the 5% level of significance.

please provide the following information.

(a) What is the level of significance? State the null and alternate hypotheses.

(b) Find the sample test statistic R, and the values of the parameters n1 and n2.

(c) Compute mR and s R and find the z-score for the sample test statistic.

(d) Conclude the test.

(e) Interpret the conclusion in the context of the problem.AppendixLO1