Chapter 14 QUIZ

14-66

TRUE OR FALSE

Question 14.200

1. True or false: The hypotheses for the Wilcoxon signed rank test for the population median of the differences are the same as those for the corresponding sign test.

Question 14.201

2. True or false: The sample size used in the Wilcoxon signed rank test always equals the number of data values in the sample.

Question 14.202

3. True or false: In the Wilcoxon rank sum test, the two samples are temporarily combined, and the ranks of the combined data values are calculated. Then the ranks are summed separately for each sample.

FILL IN THE BLANK

Question 14.203

4. A convenient graphic for assessing the symmetry of a data distribution is a ___________.

Question 14.204

5. The cutoff sample size between using the small-sample case and the large-sample case for the Wilcoxon signed rank test is ___________.

Question 14.205

6. The Kruskal-Wallis test is the nonparametric alternative to ___________ of ___________, which we learned in an earlier chapter.

SHORT ANSWER

Question 14.206

7. In the Wilcoxon signed rank test for matched-pair data, which data values need to be omitted?

Question 14.207

8. Is the Wilcoxon rank sum test used for dependent or independent samples? What about the Wilcoxon signed rank test?

Question 14.208

9. State the conditions for performing the Kruskal-Wallis test.

CALCULATIONS AND INTERPRETATIONS

Question 14.209

childhealth

10. Children Without Health Insurance. The following table contains the number of children (in thousands) who are not covered by health insurance for a random sample of 24 states. Use the sign test to test whether the population median number of children per state without health insurance is greater than 75,000, using level of significance .

State Children
without health
insurance
(1000s)
State Children
without health
insurance
(1000s)
Idaho 52 Wisconsin 63
Georgia 314 Massachusetts 103
Oklahoma 114 Illinois 302
Delaware 24 California 1225
Minnesota 104 New Mexico 93
Louisiana 170 Missouri 127
Alabama 82 New York 380
Florida 771 Ohio 157
Colorado 176 Arkansas 65
Washington 105 Connecticut 49
Pennsylvania 203 Texas 1392
Tennessee 94 Indiana 123
Table 14.116: Source: U.S. Census Bureau.

Question 14.210

carbon3

11. Carbon Emissions. The following table shows the carbon dioxide emissions (in millions of metric tons) from the consumption of fossil fuels in 2000 and 2005 for a random sample of 10 nations. Test whether the emissions have been increasing. That is, test, using a sign test, whether the population median of the difference (2005 – 2000) in carbon dioxide emissions is greater than zero, using level of significance .

Nation Carbon emissions
in 2000 (millions of
metric tons)
Carbon emissions
in 2005 (millions
of metric tons)
Brazil 342.1 360.6
Canada 558.4 631.3
China 2912.6 5322.7
France 399.0 415.3
India 994.1 1165.7
Ireland 40.4 44.1
South Africa 383.4 423.8
Thailand 160.6 234.2
Vietnam 47.4 80.4
United States 5823.5 5957.0

Question 14.211

militaryvets

12. Military Veterans. The following table contains the number of U.S. military veterans (in thousands) for a random sample of 13 states.

  1. Verify that the data are symmetric.
  2. Use the Wilcoxon signed rank test to test whether the population median number of veterans per state differs from 100,000, using level of significance .
State Veterans (1000s)
Montana 104
Vermont 55
Alaska 75
New Hampshire 132
Kansas 237
Nevada 246
Arkansas 262
South Dakota 74
West Virginia 178
Maine 144
Delaware 81
North Dakota 58
Mississippi 216

14-67

Question 14.212

13. Trade Balance. Table 20 contains the trade balance (in millions of dollars) that the United States has with a random sample of 12 European countries and a random sample of 11 Asian countries. Positive numbers indicate that our exports to that country exceed in value our imports from that country. Negative numbers indicate that exports are less than imports. Test whether the population median trade balance with European countries differs from the population median trade balance with Asian countries, using level of significance .

Table 14.119: Table 20 U.S. trade balances
European
country
Trade
balance
($ millions)
Asian
country
Trade
balance
($ millions)
Austria −7,497 Bangladesh −2,976
Belgium 10,009 China −256,207
Czech Republic −1,168 Japan −82,760
Germany −44,513 South Korea −12,918
Greece 918 Israel −7,775
Ireland −21,436 Malaysia −20,948
United Kingdom −6,629 Nepal −61
Netherlands 14,560 Thailand −14,300
Norway −4,256 Taiwan −11,968
France −14,140 Saudi Arabia −25,230
Luxembourg 475 Cambodia −2,325
Finland −2,133