For each successive presidential term from Teddy Roosevelt toRonald Reagan (first term), the party affiliation controlling the White House is shown below, where R designates Republican and D designates Democrat.

R	R	R	D	D	R	R	D	D	D	D	D
R	D	R	R	D	R

Historical Note: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.

Test the sequence for randomness.

Use= 0.05.(a)

What is the level of significance?

State the null and alternate hypotheses.

H_o: The symbols are not randomly mixed.H₁: The symbols are randomly mixed.H_o: The symbols are not randomly mixed.H₁: The symbols are not randomly mixed. H_o: The symbols are randomly mixed.H₁: The symbols are not randomly mixed.H_o: The symbols are randomly mixed.H₁: The symbols are randomly mixed.

(b)Find the sample test statisticR, the number of runs

.R=

(c)Find the upper and lower critical values in theCritical Values for Number of RunsRtable.

c₁=

c₂=