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 the5%significance level, whether an association exists between the specified pair of variables.

income and response

Short Answer

Expert verified
The null hypothesis is rejected at 5% level.
Thus, there is an association exists between income and response at the 5% significance level.

Step by step solution

01

Step 1. Given information

An association exists between the specified pair of variables income and response

The given significance=5%

02

Step 2. Check whether there is an association exists between the specified pair of variables or not.

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

03

Step 3. Use MINITAB to obtain the test statistic and p-value. 

MINITAB procedure:
Step 1: Choose Stat > Tables > Chi-Square test for association.
Step 2: In Columns containing the table, enter the column of Under $20,000,$20,000-$29,999,$30,000-$49,999and $60,000and over.
Step 3: In Rows, select Response.
Step 4: Under Statistics, select Chi-square test, Display counts in each cell, Display marginal counts and expected cell counts.
Step 5: Click OK.

04

Step 4. MINTAB output

chi-square test for Association:RESPONSE,Worksheet columns

From the MINITAB output,the value of the chi-square statistic is16.634and the p-value is0.011

05

Step 5. Conclusion for the given question

Here, theP-value is lesser than the level of significance.
That is,P-value =0.011<α==0.05.
Therefore, the null hypothesis is rejected at5%level.
Thus, there is an association exists between income and response at the5%significance level.

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Most popular questions from this chapter

Road Rage. The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggressive driving and road rage. Road rage is defined as an incident in which an angry or impatient motorist or passenger intentionally injures or kills another motorist, passenger, or pedestrian, or attempts or threatens to injure or kill another motorist, passenger, or pedestrian." One aspect of the study was to investigate road rage as a function of the day of the week. The following table provides a frequency distribution for the days on which 69 road-rage incidents occurred.

Day

Frequency

Sunday

5

Monday

5

Tuesday

11

Wednesday

12

Thursday

11

Friday

18

Saturday

7

At the significance level, do the data provide sufficient evidence to conclude that road-rage incidents are more likely to occur on some days than on others?

AIDS Cases. According to the Centers for Disease Control and Prevention publication HIV Surveillance Report, the number of AIDS cases in the United States in 2011, by region and race, is as shown in the following contingency table.

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

605225,435

a. How many cells does this contingency table have?

b. Fill in the missing entries.

c. What was the total number of AIDS cases in the United States in 2011?

d. How many AIDS cases were whites?

e. How many AIDS cases were Southerners?

f. How many AIDS cases were black Westerners?

Education of Prisoners. In the article "Education and Correctional Populations" (Bureau of Justice Statistics Special Report, NCJ 195670), C. Harlow examined the educational attainment of prisoners by type of prison facility. The following contingency table was adapted from Table 1 of the article. Frequencies are in thousands, rounded to the nearest hundred.


StateFederalLocalTotal
8th grade or less149.910.666.0226.5
some high school269.112.9168.2450.2
GED300.820.171.0391.9
High school diploma216.424.0130.4370.8
Postsecondary95.014.051.9160.9
College grad and more25.37.216.148.6
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How many prisoners

a. are in state facilities?

b. have at least a college education?

c. are in federal facilities and have at most an 8th-grade education?

d. are in federal facilities or have at most an 8th-grade education? e. in local facilities have a postsecondary educational attainment

f. who have a postsecondary educational attainment are in local facilities?

g. are not in federal facilities?

In each case, decide whether Assumptions 1and 2for using chi-square goodness-of-fit test are satisfied.

Sample size:n=50.

Relative frequencies:0.20,0.20,0.25,0.30,0.05.

US. Hospitals. Refer to Exercise 12.50.


24 or fewer25-7475 or moreTotal
General260158635575403
Psychiatric24242471737
Chronic132226
Tuberculosis0224
Other25177208410
Total310201042606580

a. Determine the conditional distribution of number of beds within each facility type.

b. Does an association exist between facility type and number of beds for U.S. hospitals? Explain your answer.

c. Determine the marginal distribution of number of beds for U.S. hospitals.

d. Construct a segmented bar graph for the conditional distributions and marginal distribution of number of beds. Interpret the graph in light of your answer to part (b),

e. Without doing any further calculations, respond true or false to the following statement and explain your answer. "The conditional distributions of facility type within number-of-beds categories are identical.

f. Determine the marginal distribution of facility type and the conditional distributions of facility type within number-of-beds categories.

g. What percentage of hospitals are general facilities?

h. What percentage of hospitals that have at least 75 beds are general facilities?

i. What percentage of general facilities have at least 75 beds?

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