For each successive presidential term from Teddy Roosevelt to Ronald 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. Ho: The symbols are not randomly mixed. H1: The symbols are not randomly mixed.Ho: The symbols are randomly mixed. H1: The symbols are not randomly mixed. Ho: The symbols are not randomly mixed. H1: The symbols are randomly mixed.Ho: The symbols are randomly mixed. H1: The symbols are randomly mixed. (b) Find the sample test statistic R, the number of runs. R = (c) Find the upper and lower critical values in the Critical Values for Number of Runs R table. c1=c2= (d) Conclude the test. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence that the sequence of presidential party affiliation is not random.Fail to reject the null hypothesis, there is insufficient evidence that the sequence of presidential party affiliation is not random. Reject the null hypothesis, there is sufficient evidence that the sequence of presidential party affiliation is not random.Reject the null hypothesis, there is insufficient evidence that the sequence of presidential party affiliation is not random.

For each successive presidential term from Teddy Roosevelt to Ronald 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. Ho: The symbols are not randomly mixed. H1: The symbols are not randomly mixed.Ho: The symbols are randomly mixed. H1: The symbols are not randomly mixed. Ho: The symbols are not randomly mixed. H1: The symbols are randomly mixed.Ho: The symbols are randomly mixed. H1: The symbols are randomly mixed. (b) Find the sample test statistic R, the number of runs. R = (c) Find the upper and lower critical values in the Critical Values for Number of Runs R table. c1=c2= (d) Conclude the test. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence that the sequence of presidential party affiliation is not random.Fail to reject the null hypothesis, there is insufficient evidence that the sequence of presidential party affiliation is not random. Reject the null hypothesis, there is sufficient evidence that the sequence of presidential party affiliation is not random.Reject the null hypothesis, there is insufficient evidence that the sequence of presidential party affiliation is not random.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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

(b)

Find the sample test statistic R, the number of runs.

R =

(c)

Find the upper and lower critical values in the Critical Values for Number of Runs R table.

c₁=c₂=

(d)

Conclude the test.

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e)

Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the sequence of presidential party affiliation is not random.Fail to reject the null hypothesis, there is insufficient evidence that the sequence of presidential party affiliation is not random. Reject the null hypothesis, there is sufficient evidence that the sequence of presidential party affiliation is not random.Reject the null hypothesis, there is insufficient evidence that the sequence of presidential party affiliation is not random.

Expert Solution

Step 1

Run test :

Run test is a statistical test used to determine of the data obtained from a sample is random. That is why it is called Run Test for Randomness.
Randomness of the data is determined based on the number and nature of runs present in the data of interest.

Given Information :

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.

From the provided data ,

Number of Republican : n₁ = 9

Number of Republican : n₂ = 9

Number of runs : R = 9

State the hypothesis :

H_o: The symbols are randomly mixed.

H₁: The symbols are not randomly mixed.

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