Chapter 14 Review Exercises

section 14.1

Question 14.172

1. What is a nonparametric hypothesis test? Explain why the term “distribution-free” may be more accurate.

Question 14.173

2. Explain why the sign test may be less efficient than the Wilcoxon signed rank test when both are compared to the test for dependent sample data.

Question 14.174

3. Why is there no efficiency rating in Table 1 (page 14-4) for the runs test?

section 14.2

Question 14.175

4. Explain the meaning of the notation in the hypotheses for the sign test for a single population median.

Question 14.176

5. Explain the meaning of the notation in the hypotheses for the sign test for matched-pair data.

For Exercises 6 and 7 do the following. (Hint: Exercise 6 represents the sign test for a single population median. Exercise 7 represents the matched-pair sign test.)

  1. Use Appendix Table I to find the value of .
  2. State the rejection rule.
  3. Calculate .
  4. Provide the conclusion and the interpretation of the hypothesis test.

Question 14.177

6. vs. , , level of significance . There are 10 pluses and 6 minuses. One data value equals 50.

Question 14.178

7. vs. , , level of significance . There are 9 pluses, 0 minuses, and 3 ties.

Question 14.179

nhlgoals

8. NHI Goals Scored. Between 2003 and 2014, the National Hockey League endured two lockout seasons and underwent a number of rules changes. Did this affect the number of goals scored? The following table shows the mean goals scored per game for a random sample of five NHL teams for the 2003-2004 and the 2013-2014 seasons. Test whether the population median of the difference in mean number of goals scored per game is greater than zero, using level of significance .

2003–2004 2013–2014
Detroit Red Wings 3.11 2.65
Tampa Bay Lightning 2.99 2.83
Phoenix Coyotes 2.29 2.56
Colorado Avalanche 2.88 2.99
Dallas Stars 2.37 2.82

14-64

Question 14.180

9. Eighth-Grade Alcohol Use. The National Institute on Alcohol Abuse and Alcoholism (NIAAA) reports on the proportion of eighth-graders who have used alcohol (Source: http://www.niaaa.nih.gov/publications). A random sample of 100 eighth-graders this year showed that 41 of them had used alcohol. Test whether the population proportion of eighth-graders who have used alcohol is less than 0.5, using level of significance .

section 14.3

Question 14.181

10. For the Wilcoxon signed rank test, what do the notations and mean?

For Exercises 11 and 12, perform the indicated Wilcoxon signed rank test for a single population median, using level of significance .

Question 14.182

11. vs. , with and .

Question 14.183

12. vs. , with , , and .

For Exercises 13 and 14, perform the indicated Wilcoxon signed rank test for the population median of two dependent samples, using level of significance .

Question 14.184

13. vs. , with and .

Question 14.185

14. vs. , with , , and .

Question 14.186

flprecipitation

15. Precipitation in Florida. The following table shows the annual precipitation (in inches) for a random sample of cities in Florida. Use the Wilcoxon signed rank test to test whether the population median annual precipitation in Florida differs from 50 inches, using level of significance .

City Annual precipitation (inches)
Gainesville 49.56
Jacksonville 51.88
Miami 58.53
Tampa 44.77
Fort Lauderdale 64.19
Orlando 48.35
Table 14.102: Source: U.S. Census Bureau.

Question 14.187

hotcoldtx

16. Hot and Cold in Texas. Is the weather in Texas on the hot side or the cold side? The following table shows the annual number of heating degree-days and cooling degree-days for a random sample of cities in Texas.17 Test, using the Wilcoxon signed rank test, whether the population median of the differences (heating degree-days minus cooling degree-days) is less than zero, using level of significance .

City Heating
degree-days
Cooling
degree-days
Austin 1648 2974
College Station 1616 2938
Dallas 2219 2878
El Paso 2543 2254
Houston 1174 3179
Killeen 2190 2477
San Antonio 1573 3038

section 14.4

For Exercises 17 and 18, test whether the population medians differ, using level of significance . The data represent two independent random samples.

Question 14.188

17.

Sample 1 24 22 28 24 33 34 38 20 32 27 32
33 34 26 22 40
Sample 2 36 25 29 23 29 34 28 32 27 38 38

Question 14.189

18.

Sample 1 71 73 59 61 68 51 60 56 59 66 67
70 62
Sample 2 59 69 68 74 62 64 60 74 50 67 54
74 73 52

Question 14.190

unemployment

19. Unemployment Rates. The following table contains the unemployment rates for independent random samples of cities in Ohio and Virginia. Test whether the population median unemployment rate differs between cities in Ohio and cities in Virginia, using level of significance .

Ohio city Unemployment
rate
Virginia city Unemployment
rate
Akron 6.6 Alexandria 2.8
Cincinnati 6.4 Charlottesville 4.6
Cleveland 7.9 Lynchburg 4.4
Columbus 5.4 Richmond 5.3
Dayton 7.6 Roanoke 4.2
Toledo 7.5 Petersburg 7.3
Virginia Beach 3.4

section 14.5

For Exercises 20 and 21, test whether the population medians differ, using level of significance . The data represent independent random samples.

Question 14.191

20.

Sample 1 11 14 17 13 18 12 10
Sample 2 17 15 15 15 18 18
Sample 3 11 19 18 12 11 12 11 15
Sample 4 21 22 20 21 23 19 17 23 24

14-65

Question 14.192

21.

Sample 1 12 15 13 16 19 12 12 15
Sample 2 12 15 18 17 17 14 20 11
Sample 3 11 17 19 17 11 12 17
Sample 4 17 19 23 21 22 20

Question 14.193

manufacturing

22. Manufacturing Workers. The following tables contain the number of workers employed in manufacturing for independent random samples of cities in Connecticut, Georgia, and Illinois. Test whether the population median number of manufacturing workers differs among the three states. Use level of significance .

Connecticut city Workers
Bridgeport 5,991
Danbury 6,553
Hartford 1,646
Middletown 4,670
New Britain 3,603
New Haven 3,253
Waterbury 4,808
Georgia city Workers
Atlanta 15,002
Athens 6,966
Columbus 11,116
Dalton 17,718
Savannah 8,679
Illinois city Workers
Danville 3,632
Champaign 2,776
DeKalb 2,205
Evanston 1,939
Peoria 4,763
Waukegan 4,780

section 14.6

For Exercises 23 and 24, you are given random samples of paired data. Perform the rank correlation test, using level of significance .

Question 14.194

23.

Sample 1 10 12 15 13 18 15
Sample 2 9 6 3 7 1 1

Question 14.195

24.

Sample 1 25 22 28 30 20 25
Sample 2 35 31 37 39 31 35

Question 14.196

hotcoldca

25. Hot and Cold in California. The following table contains a random sample of 13 cities in California, along with the average number of heating degree-days and cooling degree-days for each city. Test whether a rank correlation exists between heating degree-days and cooling degree-days, using level of significance .

California city Heating
degree-days
Cooling
degree-days
Arcadia 1295 1575
Burlingame 2720 184
Simi Valley 1822 1485
Azusa 1727 1191
Palo Alto 2584 452
Lake Forest 1465 1183
Santee 1313 1261
Torrance 1526 742
Whittier 1295 1575
Dana Point 1756 666
Camarillo 1961 389
Glendora 1727 1191
Bellflower 1211 1186
Table 14.114: Source: U.S. Census Bureau.

section 14.7

For Exercises 26 and 27, you are given sequences of data. Conduct the runs test for randomness, using level of significance .

Question 14.197

26. Y Y Y Y Y N N N N N N N Y Y Y Y Y Y Y N N N N N

Question 14.198

27. M F F M M M F F M F F M F M M M F F F M F M

Question 14.199

28. Presidential Election Winners. Since 1852, every U.S. presidential election has been won by either the Democratic Party or the Republican Party. The following sequence represents the presidential election winners since 1852, with D representing Democrat and R representing Republican.18 Test whether the sequence is random, using level of significance .

D D R R R R R R D R D R R R R D D R R R D
D D D D D R R D D R R D R R R D D R R D D