SPHU 3160 – BIOSTATISTICS IN PUBLIC HEALTH Practice Problem Set XII

August 30, 2017

Question
Practice Problem Set XII

From Gerstman, Burt B. Basic Biostatistics: Statistics for Public Health Practice, 2nd Edition, Jones & Barlett Learning, 2015.

1. Exercise 18.8, page 483

Table 18.7, page 471

Drove or rode in a car or other vehicle when driver was drinking alcohol within past 30 days by racial/ethnic group.

Oi

(Ei)

+

Total

Non-Hisp White

243

(218.24)

1911

(1935.76)

2154

Non-Hisp Black

25

(51.47)

483

(456.53)

508

Hispanic

55

(53.29)

471

(472.71)

526

Total

323

2865

3188

.0/msohtmlclip1/01/clip_image002.gif”> vs.0/msohtmlclip1/01/clip_image004.gif”>at least two pi differ

n1 = 2154, X1 =243, .0/msohtmlclip1/01/clip_image006.gif”>

n2 = 508, X2 =25, .0/msohtmlclip1/01/clip_image008.gif”>

n3 = 526, X3 =55, .0/msohtmlclip1/01/clip_image010.gif”>

.0/msohtmlclip1/01/clip_image012.gif”>,.0/msohtmlclip1/01/clip_image014.gif”>

.0/msohtmlclip1/01/clip_image016.gif”>, .0/msohtmlclip1/01/clip_image018.gif”>

.0/msohtmlclip1/01/clip_image020.gif”>, .0/msohtmlclip1/01/clip_image022.gif”>

Test Statistic .0/msohtmlclip1/01/clip_image024.gif”>

=.0/msohtmlclip1/01/clip_image026.gif”> +.0/msohtmlclip1/01/clip_image028.gif”> +.0/msohtmlclip1/01/clip_image030.gif”> +.0/msohtmlclip1/01/clip_image032.gif”>

+.0/msohtmlclip1/01/clip_image034.gif”> +.0/msohtmlclip1/01/clip_image036.gif”>

= 2.8091 + 0.3167 + 13.6130 + 1.5348 + 0.0549 + 0.0062 = 18.33

df = (r-1)(c-1) = (3-1)(2-1) =2

p-value = P(.0/msohtmlclip1/01/clip_image038.gif”>) is the largest value in Table E, page 493, for 2 degrees of freedom.

Reject H0

2. Exercise 18.9, page 483

a. Table 18.8, page 471

Oi

(Ei)

Restenosed

Did not

restenose

Total

CMV+

21

(15.0267)

28

(33.9733)

49

CMV-

2

(7.9733)

24

(18.0267)

26

Total

23

52

75

.0/msohtmlclip1/01/clip_image042.gif”> vs.0/msohtmlclip1/01/clip_image044.gif”>

.0/msohtmlclip1/01/clip_image046.gif”>,.0/msohtmlclip1/01/clip_image048.gif”>

.0/msohtmlclip1/01/clip_image050.gif”>,.0/msohtmlclip1/01/clip_image052.gif”>

Test Statistic .0/msohtmlclip1/01/clip_image054.gif”>

=.0/msohtmlclip1/01/clip_image056.gif”> +.0/msohtmlclip1/01/clip_image058.gif”> +.0/msohtmlclip1/01/clip_image060.gif”> +.0/msohtmlclip1/01/clip_image062.gif”>

= 2.3745 + 1.0502 + 4.4750 + 1.9793 = 9.88

df = (r-1)(c-1) = (2-1)(2-1) =1

p-value = P(.0/msohtmlclip1/01/clip_image064.gif”>)

.001 < p-value , and fora=.001 .0/msohtmlclip1/01/clip_image068.gif”>,

Reject H0

b. n1 = 49, X1 =21, .0/msohtmlclip1/01/clip_image070.gif”>

n2 = 26, X2 =2, .0/msohtmlclip1/01/clip_image072.gif”>

.0/msohtmlclip1/01/clip_image074.gif”>; .0/msohtmlclip1/01/clip_image076.gif”>

H0: p1=p2 vs Ha: p1?p2

Test Statistic: .0/msohtmlclip1/01/clip_image078.gif”>

.0/msohtmlclip1/01/clip_image080.gif”> =3.1435

P value = 2 P( Z> 3.14) = 2(.0008) = .0016. Reject H0.

Equivalence:

.0/msohtmlclip1/01/clip_image082.gif”>

(3.1435)2 = 9.88

“Table 18.7 presented cross-tabulated results for the number of adolescents who drove or rode in a car or other vehicle when the driver was drinking alcohol. Prevalence proportions varied from 11.3% (non-Hispanic white) to 4.9% (non-Hispanic black). Test the data in Table 18.7 for significance by calculating its chi-square statistic, df, and P-value.”

Could you please explain in great detail how to get each part of the answer, especially the P-value and the interpretation of the P-value? I have uploaded Table 18.7 and my professor’s answer key, but am still confused as to how he arrived at the interpretation of the P-value and what that interpretation even means.

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