Witte & Witte, 9e
Chapter 20
Page 1 of 6 Pages
Chapter 20: Tests for Ranked (Ordinal) Data
Exercise 1
A researcher wanted to find out if there was difference between older movie goers and
younger movie goers with respect to their estimates of a successful actor’s income. The
researcher first identified Tom Hanks as the top money maker based on data provided at
www.boxofficemojo.com. The researcher then asked a random sample of older movie
goers (50-60 years) and a random sample of younger movie goers (20-30 years) to give
their best estimate of Tom Hanks’ average earnings per film. (Tom Hanks’ average,
according to www.boxoffice.mojo.com, is $100.9 million). Carry out a nondirectional
Mann-Whitney U Test on the estimates given by the two samples to find out if the
distributions are equal. Follow the steps given below the table and use a significance
level of .05.
Estimate of Tom Hanks'
Average Earnings Per Film
(in millions)
Older Movie Goers
Younger Movie Goers
$40
$80
$50
$100
$200
$90
$8
$50
$2
$1
$10
$6
$12
$15
$15
$60
$20
$300
$50
$40
a.
b.
c.
d.
e.
f.
g.
Present the null hypothesis.
Present the alternative hypothesis.
Identify the critical value of U by referring to Table E in your textbook.
Present the decision rule.
Calculate U.
Present a statistical decision.
Present a conclusion in the context of the research situation.
Answers:
a.
b.
c.
d.
e.
H0: Population distributionOlder = Population distributionYounger
H1: Population distributionOlder ≠ Population distributionYounger
Critical U = 23
Reject H0 at the .05 level of significance if U ≤ 23.
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Chapter 20
Page 2 of 6 Pages
Ranks
Older Movie Goers
Younger Movie Goers
10.5
16
13
18
19
17
4
13
2
1
5
3
6
7.5
7.5
15
9
20
13
10.5
89
121
U1  n1n2 
n1 (n1  1)
10(10  1)
 89 = 61
 R1  (10)(10) 
2
2
U 2  n1n2 
n1 (n1  1)
10(10  1)
 121 = 29
 R2  (10)(10) 
2
2
U = 29 because it is the smaller of U1 and U2.
f. Reject H0.
g. The distributions are not equal. An inspection of the data indicates that the
younger movie goers’ estimates are higher than those of the older movie goers.
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Witte & Witte, 9e
Chapter 20
Page 3 of 6 Pages
Exercise 2
A researcher wanted to find out if there was difference between the estimates given for a
female actor’s earnings and a male actor’s earnings. The researcher hypothesized that the
estimates would be higher for a male actor than for a female actor. The researcher first
identified Tom Hanks as the top male money maker and Julia Roberts as the top female
money maker based on data provided at www.boxofficemojo.com. The researcher then
asked a random sample of movie goers to give their best estimates of Tom Hanks’
average earnings per film and Julia Roberts’ average earnings per film. (Julia Roberts’
average, according to www.boxoffice.mojo.com, is $70.1 million). Carry out a
directional Wilcoxon T Test for two related samples on the estimates to find out if the
distributions are equal. Follow the steps given below the table and use a significance
level of .05 for the directional test.
Estimate of Actors' Average Earnings Per Film
(in millions)
Tom Hanks
Julia Roberts
$1
$1
$10
$10
$15
$80
$25
$100
$200
$10
$5
$20
$100
$15
$10
$60
a.
b.
c.
d.
e.
f.
g.
h.
Present the null hypothesis.
Present the alternative hypothesis.
Determine n, the number of nonzero difference scores.
Identify the critical value of T in Table F of your textbook.
Present the decision rule.
Calculate T.
Present a statistical decision.
Present a conclusion in the context of the research situation. You may assume
that both populations have the same variability and the same shape.
Answers:
a. H0: Population distributionTom Hanks = Population distributionJulia Roberts
b. H1: Population distributionTom Hanks ≠ Population distributionJulia Roberts
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Witte & Witte, 9e
Chapter 20
Page 4 of 6 Pages
c. n = 6
Estimate of Actors' Average Earnings
Per Film
(in millions)
Tom
Julia
Difference
Hanks
Roberts
Score
$1
$1
$0
$10
$10
$0
$15
$80
-$65
$25
$100
-$75
$200
$10
$190
$5
$20
-$15
$100
$15
$85
$10
$60
-$50
d. Critical value of T = 2
e. Reject H0 at the .05 level if T ≤ 2.
f. T = 10 because it is smaller than 11.
Tom Hanks
$1
$10
$15
$25
$200
$5
$100
$10
Estimate of Actors' Average Earnings Per Film
(in millions)
Difference Ordered
Plus
Julia Roberts
Score
Scores Ranks Ranks
$1
$0
-$15
1
$10
$0
-$50
2
$80
-$65
-$65
3
$100
-$75
-$75
4
$10
$190
$85
5
5
$20
-$15
$190
6
6
$15
$85
11
$60
-$50
Minus
Ranks
1
2
3
4
g. Retain H0 at the .05 level because T = 10 is not less than 2.
h. There is no evidence that, on average, estimates of the earnings of a successful
male actor exceed that for a successful female actor.
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Chapter 20
Page 5 of 6 Pages
Exercise 3
A researcher wants to compare the salaries of registered nurses who work in California,
New York, and Florida. The researcher randomly selected several RN’s in each state and
records their annual salaries. The salaries are listed in the table shown below. Follow
states are different.
Annual Salaries
New
California
York
Florida
$40,500 $43,400 $39,250
$56,060 $45,800 $47,620
$42,350 $55,650 $48,500
$74,200 $74,200 $62,400
$65,200 $33,480 $58,200
$43,400 $55,800 $32,100
$41,900 $49,200 $34,570
$68,500
a.
b.
c.
d.
e.
f.
g.
h.
Present the null hypothesis.
Present the alternative hypothesis.
Calculate df.
Identify the critical value of H in Table D of your textbook.
Present the decision rule.
Calculate H.
Present a statistical decision.
Present a conclusion in the context of the research situation.
Answers:
a.
b.
c.
d.
e.
H0: PopulationCalifornia = PopulationNew York = PopulationFlorida
H1: H0 is false
df = number of groups – 1 = 3 – 1 = 2
Critical H = 5.99
Reject H0 at the .05 level of significance if H ≥ 5.99.
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Witte & Witte, 9e
Chapter 20
Page 6 of 6 Pages
f.
Annual Salaries
New
California
York
Florida
5
8.5
4
16
10
11
7
14
12
21.5
21.5
18
19
2
17
8.5
15
1
6
13
3
20
103
84
66
H
 (103) 2 (84) 2 (66) 2 
12  Ri2 
12

3
(
n

1
)


=
 

  3(22  1) = 1.11
n(n  1)  ni 
22(22  1)  8
7
7 
g. Retain H0 at the .05 level of significance because H = 1.11 is less than 5.99.
h. There is no evidence that RN salaries differ in California, New York, and Florida.
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