Question

Is there a relation between murder and arson? A random sample of 15 Midwest cities (over 10,000 population) gave the following information about annual number of murder and arson cases. (Reference: Federal Bureau of Investigation, U.S. Department of Justice.) City 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Murder 23 10 21 17 22 7 6 9 8 20 18 12 19 11 13 Arson 104 37 121 111 174 26 18 6 13 163 71 66 87 135 93 Use a 1% level of significance to test the claim that there is a monotone-increasing relationship between the ranks of murder and arson. (a) Rank-order murder using 1 as the largest data value. Also rank-order arson using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test. City Murder Rank x Arson Rank y d = x - y d2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Σd2 = (b) What is the level of significance? Correct: Your answer is correct. State the null and alternate hypotheses. Ho: ρs = 0; H1: ρs ≠ 0 Ho: ρs = 0; H1: ρs < 0 Ho: ρs = 0; H1: ρs > 0 Ho: ρs < 0; H1: ρs = 0 Correct: Your answer is correct. (c) Compute the sample test statistic. (Use 3 decimal places.)

Answer #1

a)

Using rank order 1 as the largest data value

Here is the table of ranks

spearman rank correlation is

= 1- (6*122 / 15*(225-1) )

= **0.7821**

b)

Level of significance is **0.01**

Hypothesis

null hypothesis

alternate hypothesis

c)

Test statistic is

Here

r = Spearman rank correlation = 0.7821

= **4.5252**

Is there a relation between incidents of child abuse and number
of runaway children? A random sample of cities (over 10,000
population) gave the following information about the number of
reported incidents of child abuse and the number of runaway
children. (Reference: Federal Bureau of Investigation, U.S.
Department of Justice.) City 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Abuse cases 31 36 77 78 73 57 35 108 81 11 111 24...

Is there a relation between police protection and fire
protection? A random sample of large population areas gave the
following information about the number of local police and the
number of local fire-fighters (units in thousands). (Reference:
Statistical Abstract of the United States.)
Area
1
2
3
4
5
6
7
8
9
10
11
12
13
Police
10.4
16.3
16.7
16.9
17.9
3.8
15.0
12.5
17.4
11.8
6.7
5.0
4.7
Firefighters
1.7
4.0
4.8
4.5
3.5
1.2
2.5
1.8...

Random collections of nine different solutions of a calcium
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6 7 8 9 10 11 12
Rank by Professor A 6 10 2 1 5 11 4 3 7 12 9 8
Rank by Professor B 5 11 6 3 4 12 2 1 7 10 8 9
The P-value for testing the significance of rank-correlation
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The Spearman...

Test the hypothesis that most cereals have nine or less grams of
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Sugars
6
8
5
0
8
10
14
8
6
5
12
1
9
7
13
3
2
12
13
7
0
3
10
5
13
11
7
10
12
11
10
6
9
3
13
7
10
14
0
0

Cork price: 16 10 15 10 17 11 14 13 11 14 11 16 18 16 10 17 14
14 16 7 10 12 19 15 16 14 9 12 21 13 10 16 12 16 13 17 17 13 14 18
11 12 15 16 13 18 16 17 12 12 14 9 11 14 19 13 11 17 11 13 15 14 18
18 18 12 10 11 13 14 11 14 18 13 13 19 17 14...

A data processing company has a training program for new
salespeople. After completing the training program, each trainee is
ranked by his or her instructor. After a year of sales, the same
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to net value of the contracts they have acquired for the company.
The results for a random sample of 11 salespeople trained in the
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# of text messages sent yesterday
3 8 3 18 2 1 8 1 6 13 15 14 13 9 20 12 5 9 18 18 13 2 7 6 0 0 11
12 4 13 1 19 4 12 4 11 8 18 1 15 12 6 6 12 19 12 20 12 8 12
Test the following claim:
70% of individuals that send text messages send less than 10
messages per day, α = 0.01

Is there enough evidence that the average number of PURPLE
Skittles in a package is greater than the average number of ORANGE
Skittles in a package? Use the attached Skittles sample and test at
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Package
Red
Orange
Yellow
Green
Purple
Total
Dominant Color
1
15
15
16
12
14
72
Y
2
13
6
11
16
15
61
G
3
9
9
10
18
15
61
G
4
7
9
8
18
15
57
G...

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