Answered: The majority party of the United States…

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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The majority party of the United States House of Representatives for each term (bi-annual) from 1973 to 2007 is shown below, where D and R represent Democrat and Republican, respectively. (Reference: Statistical Abstract of the United States.)

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

(b) Find the sample test statistic R, the number of runs.

(c) Find the upper and lower critical values in Table 10 of Appendix II.

c₁
c₂

(d) Conclude the test.

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.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 fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the sequence of party affiliation for U.S. House of Representatives is not random.Fail to reject the null hypothesis, there is sufficient evidence that the sequence of party affiliation for U.S. House of Representatives is not random. Fail to reject the null hypothesis, there is insufficient evidence that the sequence of party affiliation for U.S. House of Representatives is not random.Reject the null hypothesis, there is insufficient evidence that the sequence of party affiliation for U.S. House of Representatives is not random.

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