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Chapter 12: Q. 12.57 (page 502)

In each of exeercises 12.57-12.59, use the technology of your choice to solve the specified problems.

The National Governors Association publishes information on U.S Governors in Governors' Political Afflitiation and Term of Office. Based on that document we obtain the data on region of reidence an political party given on WeissStats site.

a. Group the bivariate data for these two variables into a contingency table.
b. Determine the conditional distribution of region within each party and the marginal distribution of region.
c. Determine the conditional distribution of party within each region and the marginal distribution of party.
d. Are the variables "region" and "party" for U.S. governors associated? Explain your answer.

Short Answer

Expert verified

(a) The bivariate data for these two variables into a contingency table is:

(b) The conditional distribution of region within each party and the marginal distribution of region is:

(c) The the conditional distribution of party within each region and the marginal distribution of party is:

(d) Yes, the variables "region" and "party" for U.S. governors are associated beacuse the conditional distribution of each party are not similar.

Step by step solution

01

Part (a) Step 1. Given Information.

The data on region of reidence an political party given on WeissStats site.

02

Part (a) Step 2. Use MINITAB procedure.

By using MINITAB procedure,

1. Choose stat > tables > Cross tabulation and Chi-square.

2. Select Raw data.

3. In rows, select region, and in columns select party.

4. Under display, select counts.

5. Click OK.

03

Part (a) Step 3. MINITAB output.

Tabulated statistics: Region (Rows), Party (Columns)


DemocratRepublicanAll
MIdwest3912
Norteast639
South61016
West6713
All212950
04

Part (b) Step 1. Use MINITAB.

By using MINITAB procedure,

1. Choose stat > tables > Cross tabulation and Chi-square.

2. Select Raw data.

3. In rows, select region, and in columns select party.

4. Under display, select column percent.

5. Click OK.

05

Part (b) Step 2. MINITAB output.

Tabulated statistics: Region (Rows), Party (Columns)


DmocrateRepublicanAll
Midwest14.2931.0324
Northeast28.5710.3418
South28.5734.4832
West28.5724.1426
All100100100

Cell contents: % of columns.

06

Part (c) Step 1. Use MINITAB. 

By using MINITAB procedure,

1. Choose stat > tables > Cross tabulation and Chi-square.

2. Select Raw data.

3. In rows, select region, and in columns select party.

4. Under display, select row percent.

5. Click OK.

07

Part (c) Step 2. MINITAB output.

Tabulated statistics: Region (Rows), Party (Columns)


DemocratRepublicanAll
Midwest2575100
Northeast66.6733.33100
South36.5062.50100
West46.1553.85100
All4258100

Cell contents: % of rows.

08

Part (d) Step 1. Relation between "region" and "party".

Yes, the variables "region" and "party" for U.S. governors are associated beacuse the conditional distribution of each party are not similar.

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Most popular questions from this chapter

Girls and Boys. One probability model for child gender is that a boy or a girl is equally likely to be born. If that model is correct, then, for a two-child family, the probabilities are 0.25,0.50, and 0.25 for two girls, one girl and one boy, and two boys, respectively. W. Stansfield and M. Carlton examined data collected in the National Health Interview Study on two-child families in the article "The Most Widely Published Gender Problem in Human Genetics" (Human Biology, Vol. 81, No. 1, pp. 3-11). Of 42,888 families with exactly two children, 9,523 had two girls, 22,031 had one girl and one boy, and 11,334 had two boys.

a) At the 1% significance level, do the data provide sufficient evidence to conclude that the distribution of genders in two-children families differs from the distribution predicted by the model described?

b) In view of your result from part (a), what conclusion can you draw?

Although the chi-square homogeneity test and the chi-square independence test use essentially the same basic procedure, the context of the two tests are quite different. Explain the difference.

We have presented a contingency table that gives a cross-classification of a random sample of values for two variables x and y, of a population.

Perform the following tasks

a. Find the expected frequencies Note: You will first need to compute the row totals, column totals, and grand total.

b. Determine the value of the chi-square statistic

c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.

12.53 AIDS Cases. Refer to Exercise 12.47. For AIDS cases in the United States in 2011, solve the following problems:

RegionWhiteBlackOtherTotal
Northeast1,1002,493
5,177
Northwest1,137
5043221
South2,7617,848
12,867
West
76417664,230
Total

605225,435

a. Find and interpret the conditional distributions of region by race.

b. Find and interpret the marginal distribution of region.

c. Are the variables "region" and "race" associated? Explain your answer.

d. What percentage of AIDS cases were in the South?

e. What percentage of AIDS cases among whites were in the South?

f. Without doing further calculations, respond true or false to the distributions of race by region are not identical.

g. Find and interpret the marginal distribution of race and the conditional distributions of race by region.

A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values. What are the degrees of freedom for the x2-statistic?
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