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Chapter 12: 12.87 (page 512)

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

Short Answer

Expert verified

The null hypothesis is not rejected at 5% level.

There is no association between gender and response at the 5% significance level.

Step by step solution

01

Step 1. Given information 

The given significance level5%

The given specified pair of variables= gender and response

02

Step 2. Check whether or not there is association exists between age and response at 5% significance level. 

Step 1:
The test hypotheses are given below:
Null hypothesis:
H0 : There is no association exists between age and response.
Alternative hypothesis:
H1 : There is an association exists between age and response.

03

Step 3.  Finding the level of significance 

Here, the level of significance is, 5%

04

Step 4. Find the expected frequency and test statistic. 

MINITAB procedure:
Step 1: Choose Stat > Tables > Chi-Square Test (Two-Way Table in Worksheet).
Step 2: In Columns containing the table, enter the columns of male and female.
Step 3: In rows, select response
Step 4: Click OK.

05

Step 5. Finding the MINITAB output 

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Most popular questions from this chapter

In each of Exercises 12.11-12.16, we have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fir text and the sample size. In each case, decide whether Assumptions 1 and 2 for using that text are satisfied.

Sample size : n= 100.

Relative frequencies: 0.44 , 0.25 , 0.30 , 0.01.

Housing Foundations. The U.S. Census Bureau publishes information about housing units in American Housing Survey for the United States. The following table cross-classifies single-unit occupied housing units by foundation type and tenure of occupier. The frequencies are in thousands.

For single-unit occupied housing units:


OwnerRenterTotal
Full-basement22,9873,30126,288
Partial-basement7,5169908,506
Crawl-space14,2893,47717,776
Concrete slab21,0135,65126,664
Other9493341,283
Total66,75413,75380,507

a. How many have crawl spaces?

b. How many are owner occupied?

c. How many are rented and have full basements?

d. How many have a basement?

e. How many are either owner occupied or have a concrete slab?

In Exercises 12.101-12.106, tase either the critical-value approach or the P-value approach to perform a chi-square homogeneity test, provided the conditions for using the test are met.
12.101 Self-Concept and Sightedness. Self-concept can be defined as the general view of oneself in terms of personal value and capabilities. A study of whether visual impairment affects self-concept was reported in the article "An Exploration into Self Concept: A Comrarative Analysis between the Adolescents Who Are Sighted and
Elind in India" (British Journal of Visual Impairment, Vol. 30, No. 1, of sighted and blind Indian adolescents gave the following data on self-concept.

a. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in self-concept distributions between sighted and blind Indian adolescents?
b. Repeat part (a) at the1%significance level.

Loaded Die? A gambler thinks a die may be loaded, that is, that the six numbers are not equally likely. To test his suspicion, he rolled the die 150 times and obtained the data shown in the following table.

Number

1

2

3

4

5

6

Frequency

23

26

23

21

31

26


Do the data provide sufficient evidence to conclude that the die is loaded? Perform the hypothesis test at the 0.05 level of significance.

Presidential Election. According to Dave Leip's Atlas of U.S. Presidential Elections, in the 2012 presidential election, 51.01%of those voting voted for the Democratic candidate (Barack H. Obama), whereas 57.50%of those voting who lived in Illinois did so. For that presidential election, does an association exist between the variables "party of presidential candidate voted for" and "state of residence" for those who voted? Explain your answer.
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