Section 14.4 Exercises

CLARIFYING THE CONCEPTS

Question 14.71

1. What do we mean when we say that we have two independent samples? (p. 14-30

Question 14.72

2. Which hypothesis test did we learn about in Section 10.2 that examined the difference in population means for two independent samples? What were the conditions for this test? Are the conditions for the Wilcoxon rank sum test stricter or less strict? (p. 14-29

Question 14.73

3. True or false: When performing the Wilcoxon rank sum test, it is not necessary to find the sum of the ranks for the second sample, . (p. 14-30

Question 14.74

4. Clearly explain the meaning of and . (p. 14-30

Question 14.75

5. If the null hypothesis is true, what do we expect regarding and ? (p. 14-30

Question 14.76

6. What are the requirements for performing the Wilcoxon rank sum test? (p. 14-30

PRACTICING THE TECHNIQUES

image CHECK IT OUT!

To do Check out Topic
Exercises 7–10 Example 13 Finding and summing the
ranks of combined data
Exercises 11–14 Example 14 Performing the Wilcoxon
rank sum test for two
independent samples

For Exercises 7–10, calculate , the sum of the ranks for the first sample. The data represent two independent random samples.

Question 14.77

7.

Sample 1 4 3 5 4 7 9 2 9 2 3 5
Sample 2 11 7 5 3 10 8 6 3 3 4 5 3

Question 14.78

8.

Sample 1 6 5 9 11 6 12 7 12 8 10 8 6
Sample 2 20 19 16 20 19 11 20 10 10 11 11

Question 14.79

9.

Sample 1 96 98 81 94 89 88 84 88 84 80 81 97
Sample 2 97 97 86 90 82 85 96 81 85 79 79 80 96 83

Question 14.80

10.

Sample 1 565 544 509 523 598 525 521 530
523 544 589 589
Sample 2 532 572 589 544 601 548 561 539
578 549 582

For Exercises 11–14, we are interested in whether the population medians differ. Do the following:

  1. State the hypotheses.
  2. Find the critical value and state the rejection rule.
  3. Find the value of the test statistic .
  4. State the conclusion and the interpretation.

Question 14.81

11. Use the data and the value you calculated for in Exercise 7. Use level of significance .

Question 14.82

12. Use the data and the value you calculated for in Exercise 8. Use level of significance .

Question 14.83

13. Use the data and the value you calculated for in Exercise 9. Use level of significance .

Question 14.84

14. Use the data and the value you calculated for in Exercise 10. Use level of significance .

APPLYING THE CONCEPTS

14-35

Question 14.85

facebook

15. Facebook Game Pages. The following table shows the number of fans for independent random samples of Facebook pages for games and Facebook pages for television shows as of February 11, 2009. Test whether the population median number of fans of Facebook pages for games differs from the population median number of fans of Facebook pages for television shows, using level of significance . The data are shown in thousands.

Table 14.50: Number of fans of facebook game and Facebook television show pages
Facebook game
page		 Fans
(1000s)		 Facebook TV
show page		 Fans
(1000s)
Guitar Hero 640 House 1445
World of Warcraft 167 American Idol 377
Pro Evolution Soccer 497 Grey's Anatomy 1244
Grand Theft Auto 4 459 Gossip Girl 981
Texas Hold 'em
Poker		 191 Futurama 546
Need for Speed 248 Lost 379
Crash Bandicoot 394 South Park 146
Call of Duty 4 227 CSI: Miami 363
Final Fantasy Series 197 Family Guy 855
Mario Kart 399 The Office 567
The Sims 2 568 Mythbusters 545
The Simpsons 807
Table 14.50: Source: allfacebook.com.

Question 14.86

carbon2

16. Carbon emissions. Independent random samples of European and African nations were taken, and the carbon dioxide emissions from fossil fuels were recorded (in millions of metric tons). Test whether the population median carbon emissions per nation in Europe differs from that of the nations in Africa, using level of significance .

Table 14.51: Carbon emissions from European and African nations
European
nation		 Carbon
emissions		 African
nation		 Carbon
emissions
Belgium 147.58 Algeria 88.23
Czech Republic 116.30 Congo 5.53
Denmark 59.13 Egypt 151.62
France 417.75 Ethiopia 5.13
Germany 857.60 Kenya 10.79
Greece 107.07 Mozambique 4.98
Ireland 46.86 Rwanda 0.83
Italy 468.19 South Africa 443.58
Poland 303.42 Sudan 12.26
Portugal 61.71 Tanzania 4.68
Spain 372.62 Zimbabwe 10.33
United Kingdom 585.71
Table 14.51: Source: U.S. Energy Information Administration, 2008.

Question 14.87

propertytax

17. Property Taxes. You want to move to either a small town in Ohio or a small town in North Carolina. You did some research on property taxes in each state and chose the two independent random samples shown in the table below. The data represent the property taxes in dollars for a residence assessed at $250,000. Test whether the population median property tax in Ohio differs from that in North Carolina, using level of significance .

Ohio 270 315 177 245 180 292 291 298
270 165 400 268 289 285 225
North Carolina 206 129 176 120 154 123 164 147
207 138 143 201
Table 14.52: Source: U.S. Census Bureau.

Question 14.88

flvs.tx

18. Florida Cities versus Texas Cities. Does the metropolitan-level gross domestic product differ for cities in Florida versus cities in Texas? Independent random samples of Florida and Texas cities were drawn, and the gross domestic product of the cities was recorded. Test whether the population median metropolitan-level gross domestic product differs for cities in Florida versus cities in Texas, using level of significance .

Table 14.53: Gross domestic product for cities in Florida and Texas
Florida city GDP
($ millions)		 Texas city GDP
($ millions)
Sarasota 24,772 Abilene 4,927
Fort Myers 21,838 Amarillo 8,435
Daytona Beach 11,919 Austin 71,176
Gainesville 8,903 College Station 5,669
Jacksonville 58,163 Corpus Christi 14,352
Miami 248,029 Dallas 338,493
Orlando 97,384 El Paso 23,563
Pensacola 13,040 Houston 344,516
Tallahassee 12,152 San Antonio 72,738
Tampa-St.
Petersburg		 108,520 Port Arthur 13,476
Winter Haven 17,309 Brownsville 6,555
Killeen 12,286
Table 14.53: Source: U.S. Bureau of Economic Analysis.

14-36

Question 14.89

phospotassium

19. Phosphorus and Potassium in Food. The following data represent independent random samples taken from a population of food items, recording the amount of phosphorus in the first sample and the amount of potassium in the second sample (both measurements are in milligrams). Test whether the population median amount of phosphorus differs from the population median amount of potassium, using level of significance .

Phosphorus (mg) 424 14 36 121 395 0 927 222 143
97 66 31 140 142 0 110 89 131
54 71 7 129 56 117 34
Potassium (mg) 106 387 627 237 66 31 50 103 18
265 271 62 17 132 302 7 336
292 298 278
Table 14.54: Source: U.S. Department of Agriculture.

Question 14.90

gacaincome

20. Income in California and Georgia. The following table contains the per capita personal income for independent random samples of counties in California and Georgia. Test whether the population median per capita personal income per county differs for California versus Georgia, using level of significance .

Table 14.55: Income in California and Georgia
California
county		 Per capita
personal
income ($)		 Georgia
county		 Per capita
personal
income ($)
Alameda 45,689 Treutlen 18,840
Ventura 42,746 Effingham 28,443
Napa 47,491 Echols 19,171
Solano 35,074 Wilcox 21,546
Yolo 31,990 Whitfield 29,838
Tulare 24,153 Monroe 30,352
San Benito 32,472 Fannin 25,020
Colusa 25,201 Henry 26,876
Santa Clara 55,735 Liberty 24,216
Monterey 38,373 Stephens 25,931
Shasta 30,762 Dooly 21,228
San Mateo 66,839
Table 14.55: Source: U.S. Bureau of Economic Analysis.