Discuss the below:
Q-Wilcoxon-Signed Rank Test
The 1997 price/earnings ratios for a sample of 12 stocks are shown in the following list (Barron's, December 8, 1997). Assume that a financial analyst has provided the estimated price/earnings ratio for 1998. Using a .05 level of significance, what is your conclusion about the differences between the price/earnings ratios for 1997 and 1998?
D1 denotes probability distribution of 1997 P/E Ratios
D2 denotes probability distribution of 1998 P/E Ratio
H0 : D1 and D2 are identical probability distributions
Hα: D1 is shifted to the right or left of D2, in other words, the two probability distributions are not identical. This is a two-sided test.
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COMPANY
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1997 P/E RATIO
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1998 P/E RATIO
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Coca-Cola
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40
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32
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Du Pont
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24
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22
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Eastman Kodak
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21
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23
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General Electric
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30
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23
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General Mills
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25
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19
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IBM
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19
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19
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McDonalds
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20
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17
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Merck
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29
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19
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Motorola
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35
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20
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Philip Morris
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17
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18
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Walt Disney
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33
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27
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Xerox
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20
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16
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Wilcoxon Signed Ranks Test
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X1
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X2
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Diff
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|Diff|
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Rank
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H0 :
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m1 = m2
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m1 >= m2
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m1 <= m2
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40
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32
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8
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8
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9
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S(+)
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62.5
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T
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3.5
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62.5
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3.5
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24
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22
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2
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2
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2.5
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S(-)
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3.5
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p-Value
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21
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23
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-2
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2
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2.5
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Look up T tables for p-Values
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30
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23
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7
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7
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8
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n
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11
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25
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19
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6
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6
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6.5
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19
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19
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0
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E[T]
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33
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p ≤ 0.004883
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20
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17
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3
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3
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4
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s(T)
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29
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19
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10
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10
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10
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35
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20
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15
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15
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11
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17
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18
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-1
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1
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1
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33
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27
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6
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6
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6.5
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20
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16
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4
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4
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5
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