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Chapter 12: Q. 12.46 (page 500)

Part (a): Group the bivariate data for these two variables into a contingency table.

Part (b): Determine the conditional distribution of class level within each political party affiliation.

Part (c): Are the variables "political party affiliation" and "class level" for this population of night school students associated? Explain your answer.

Part (d): Without doing further calculation, determine the marginal distribution of class level.

Part (e): Without doing further calculation, respond true or false to the following statement and explain your answer: "The conditional distributions of political party affiliations class levels are identical to each other and to the marginal distribution of political party affiliations".

Short Answer

Expert verified

Part (a): The contingency table is given below,

Part (b): The conditional distribution is given below,

Part (c): No, because the conditional distribution of class level for all values of "party affiliation" are identical.

Part (d): The marginal distribution of class level is fresh 0.1, junior 0.4, senior 0.2and sophomore 0.3.

Part (e): True, as the two variables "political party affiliation" and "class level" are not associated as the table in part (b) shows.

Step by step solution

01

Part (a) Step 1. Given information,

Consider the given question,

02

Part (a) Step 2. Write the contingency table.

On grouping the bivariate data for the two variables "political party affiliation" and "class level" into a contingency table is given below,

03

Part (b) Step 1. Determine the conditional distribution of gender.

The table of required conditional distribution within each political part affiliation is given below,

04

Part (c) Step 1. Explain if an association exist.

No, there is no association between the two variables "political party affiliation" and "class level" for this population of night school students.

As the conditional distribution of class level for all values of "party affiliation" are identical.

05

Part (d) Step 1. Determine the marginal distribution.

Without any calculation, the marginal distribution of class level is given below,

As there is no association between the two given variables.

06

Part (e) Step 1. Explain if the statement is true or false.

The statement is true.

Because the two variables "political party affiliation" and "class level" are not associated as the table in part (b) shows.

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Most popular questions from this chapter

Job Satisfaction. A CNN/USA TODAY poll conducted by Gallul asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among which were gender, age, type of community, educational attainment, income, and type of employer. The data are provided on the WeissStats site. In each of Exercises 12.87-12.92, use the technology of your choice to decide, at the 5% significance level, whether an association exists between the specified pair of variables.

Gender and response

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.

P.Noakes et al. researched the effects of fatty acids found in oily fish on lowering the risk of allergic disease in the article "Increased Intake of Oily Fish in Pregnancy: Effects on Neonatal Immune Responses and on Clinical Outcomes in Infants at 6Mo.". Pregnant women were randomly assigned to continue their habitual diet (control group), which was low in oily fish, or to consume two portions of salmon per week (treatment group). Their infants were clinically evaluated at 6months of age and the frequency of many different symptoms was recorded. Of the 37infants in the control group,12had symptoms of dry skin; and of the 45 infants in the experimental group, 14had symptoms of dry skin. At thedata-custom-editor="chemistry" 5%significance level, do the data provide sufficient evidence to conclude that a difference exists in the proportions of infants who have symptoms of dry skin at6 months between those whose mothers continue their habitual diet and those whose mothers consume two portions of salmon per week?

Part (a): Use the two-portionsz-test to perform the required hypothesis test.

Part (b): Use the chi-square homogeneity test to perform the required hypothesis test.

Part (c): Compare your results in parts (a) and (b).

Part (d): Explain what principle is being illustrated.

In this exercise, you are to consider two variables, xand ydefined on a hypothetical population. Following are the conditional distributions of the variable ycorresponding to each value of the variablex.
a. Are the variables xandy associated? Explain your answer.
b. Determine the marginal distribution ofy.
c. Can you determine the marginal distribution of x? Explain your answer.

We stated earlier that, if two variables are not associated, ther eis no point in looking for a casual relationship. Why is that so?
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