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Unformatted text preview: Chapter 13 Nonparametric Statistics 13 1 Overview 13—2 Sign Test
P 695 1,3,9,11 13—3 Wilcoxon Signed — Ranks Test for Matched Pairs
P 702 1,3,5,7 13~4 Wilcoxon Signed —— Sum Test for TWO Independent Samples
P 708 3,4 13~5 KruskalWallis Test
P 716 1,4,5 I 13—7 Run Test for Randomness
P 736 5,7,9,13 Overview
Sign Test
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Section 13—2 1. The test statistic of x = 3 is not less than or equal to the 9. ”ii. 13. entice! value of 1. There is not sufficient evidence to sup»
port the claim that there is a difference between report—
ed and measured heights of female statistics students. . Convert x a 301 to the test statistic z = ~42.61. Criticai value: 2 = ~1 .645 (assuming a 0.05 significance ievel}.
There is sufficient evidence to support the claim that the
majority of people say that they voted in the election. . Convert x=i to the test statistic z== —5.32. Critical value: 2 = 1.645 {assuming a 0.05 significance Eevel).
There is sufficient evidence to support the claim that the
Coke cans have volumes with a median greater than 12 oz. . {instead of a right—tailed test to determine whether x = 18 is iarge enough to be significant, use a ieft—tailed
test to determine whether x m 15 is small enough to be
significant.) Convert x = 15 to the test statistic
z m “0.35. Critical vaiue: z = ~1 .645. There is not suffi—
cient evidence to support the claim that the median is
greater than 0.9085 g. The test statistic of x a 1 is less than or equal to the
critical vaiue of 2. There is sufficient evidence to warrant rejection of the ciaim of no difference between the
right— and left~hand reaction times. Convert X m 8 to the test statistic am —2.83. Critical
values: 2 m $2.575. There is sufficient evidence to war rant rejection of the claim that the drinks had no effect
on reaction tirnes. First approach: 2 = —1.90; reject Ho.
Second approach: 2 = —1.73; reiect Ho.
Third approach: 2 m 0; fail to reject Ho. 15. *,*, *, *, *,0,0,0,1,i.1,2,2,3,3 Section 133 1. Test statistic: T2 9.5. Criticai value: T m 3. Fail to reject
the null hypothesis that both samples come from the
same population distribution. 3. Test statistic: Tm 4.5. Critical vaiue: T m 21. Reject the null hypothesis that both samples come from the same
population distribution. 5. Test statistic: T e 5.5. Critical value: T2 13. Reject the null hypothesis that both samples come from the same population distribution. There is sufficient evidence to support the claim that there is a difference between the
two times. . Test statistic: T: 0. Critical value: T= 14 (assuming a 0.05 significance level). Reject the null hypothesis that
both samples come frorn the same population distribu tion. There is sufficient evidence to support the ciaim
that the drug has an effect. . a. O, 27.5 b. 0, 637.5'
c. 1954 Section 134 1 . p” = 577.5, 0;; a 56.358, H = 569, z = —o.15. Test
statistic: z = O.15. Criticai vaiues: z = $1.96. Fail to
reject the nuil hypothesis that red and brown M&Ms have weights with identical popuiations. They appear to
be the same. . [in = 350,0;1 = 17.321, 5’ m 96.5, 2 = —3.09. Test STE" tistic: z w ~3.09. Critical vaiues: z w "12.575. "There is
sufficient evidence to warrant rejection of the claim that
the two samples come from ldenticai populations. flag as 1314, 0'3 = 88.792, R a“— 1958, 2: 7.25. Test stew
tistic: z m 7.25. Criticai vaiues: z M $1.86 {assuming a
0.05 significance level). There is sufficient evidence to
support the claim that the two samples come from diffen
ent popuiations. The sugar in reguiar coke weighs more. .pﬁ. =1330,cr,q a 94.383, Fr: 1153. 2a Min. Test statistic: z = —1.77. Criticai vaiues: z = $1.96 iassurn»
ing a 0.05 significance ievel). There is not sufficient evi dence to'support the claim that new textbook prices are
different at the two colleges. 9. The resolts are the serne. ‘l. . z = 0.74; the test statistic is the same number with opposite sign. Section 135 Test statistic: H= 14.431. Critical vaiue: X2 a 7.815.
There is sufficient evidence to warrant rejection of the ciaim that the different years have time intervais with
identical populations. . Test statistic: H 2 4.234. Criticai vaiue: X2 = 7.815 (assuming a 0.05 significance ieveli. There is not suffi
cient evidence to support the ciaim that left femur loads
for the four car weight categories are not all the same.
{They are not significantly different.) Test statistic: H = 6.631. Criticai value: x2 = 5.991. There
is sufficient evidence to warrant rejection of the ciaim that
the three samples come from identicai populations. '1'. $est statistic: H = 2975. Critical vaiee: x2 m 11.071.
There is not sufficient evidence to warrant rejection of
the cieim that the weights are the same tor each of the
six different coior populations. 9. a. “the test statistic H does not change. b. The test statistic H does not change.
c. The value of the test statistic does not change much
{because the rank is used instead of the magnitude of
the outlier}. r
3?. ST W 366; adjusted H m 14.431335 + 099868910,
which is 14.479. Change is not substantial. Section 13 ~7 3. n1 2 10, n2 "—M 5, G m 3, 5% cutoff values: 3, 12; reject
randomness. 3. n1 = 8, n2 m 12. G = 6, 5% cutoff valees: 6, 16; reject
randomness. _ s. n. = 1’2, n2 m a. e m 10.5% cutoff values: a, 15; tel: to
reject randomness. 7. R1 = 35, ti; = i3, G = 32, 5% cutoff values: 9, 21; fall
to reject randomness. 9. n1 2 17, n2 m 14, (3 m 14, 5% cutoh‘ values: 10, 23; fall
to reject randomness. 11. The median corresponds to July 2; n. = 6, n2 = 6, G e 2, 5% cutoff Values: 3, ii; reject randomness. 13. n, = 49, n: = 51, G n 48. Leg = 50.98, as a 4.9727.
Test statistic: z 5—160. Criticai values: 2 = "£1.98. Feii
to reject randomness. “:5. n1 = 34,171 = at, G a 3541.6 = 33.431, ch w 3.9909.
Test statistic: z i 0.39. Critical values: z= $1.96. Fail
to reject randomness. 17. Minimum is 2, maximum is 4. Critical vetoes of 1 and 6 can never be realized so that the nuii hypothesis of ren
domness can never be rejected. ...
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