1. In a study of hypertension amd taste acuity, one variable of interest was smoking status.

Of the 7 persons in the hypertensive group, 4 were smokers. The control group of 21

normotensive persons included 7 smokers. Is there a different in the proportion of

smokers in the two groups at the 0,05 level of significant?

Diketahui :

X1 = 4 X2 = 7

N1 = 7 N2 = 21

α = 0,05

Jawaban :

a. Ho : tidak ada perbedaan proporsi perokok yang hipertensi dengan normotensi

Ha : ada perbedaan proporsi perokok yang hipertensi dengan normotensi

b. α = 0,05

c. P’ = X1 + X2 = 11 = 0,4

N1 + N2 28

SE =

=

= 0,2

Uji Z

Z = P1-P2

SE

= 0,6 – 0,3 = 1,5

0,2

Z = 1,5 = 0,4332

Pv = 0,5 – 0,4332 = 0,0668

Pv > α Ho gagal ditolak

d. Tidak ada perbedaan yang signifikan antara proporsi perokok yang hipertensi dengan

normotensi

2. Of 186 participans in a program to control heart disease, it was discovered that 102 had

education beyond secondary school. Does this indicate that the program is attracting a

more highly educated group of people than world be expected, given that 25% of the US

population has education beyond secondary school? Use α=0,01?

3. In a dental study of a tie between infant occlusion and feeding methods, there were 27

breast-fed and 60 bottle-fed infants. It was noted that 7 of the breast-fed babies and 26 of

the bottle-fed babies developed a related open-bite gum pad in the first 4 months of life.

Would you conclude that the bottle-fed group showed a higher proportion of the open-

bite gum pad problem? Use α = 0,05.

Diketahui :

X1 = 7 X2 = 26

N1 = 27 N2 = 60

α = 0,05

Jawaban :

a. Ho : Tidak ada perbedaan proporsi antara pertumbuhan gusi anak menyusui dengan

ASI dan proporsi anak menyusui dengan botol.

Ha : Ada perbedaan proporsi antara pertumbuhan gusi anak menyusui dengan ASI

dan proporsi anak menyusui dengan botol

b. α = 0,05

c. P’ = X1 + X2 = 7 + 26 = 33 = 0,38

N1 + N2 27 + 60 87

SE =

=

= 0,11

Uji Z

Z = P1-P2

SE

= 0,26 – 0,43 = 1,54

0,11

Z = 1,54 = 0,4382

Pv = 0,5 – 0,4382 = 0.06

Pv > α Ho gagal ditolak

d. Tidak ada perbedaan yang signifikan antara proporsi pertumbuhan gusi anak

menyusui dengan ASI dan proporsi anak menyusui dengan botol

4. Public health official found that, in a random sample of 100 men in a small community,

13 were infected with AIDS.

a. Obtain an estimated of the proportion of men infected with AIDS in that community

b. Calculate the 95% CI for π, the true proportion of men infected with AIDS

Diketahui :

X = 13

N = 100

CI = 95%

Jawaban :

SE = = = 0,03

π = p + X1/2α x SE

= 0,13 + 1,96 x 0,03

= {0,07 ; 0,19}…CI 95%

5. A random check of drivers on busy highway revealed that 60 out of 100 male drivers and

70 out of 100 female drivers were wearing their seatbelts.

a. Obtain estimate of the proportion of male and female drivers who wear seatbelts

b. Construct a 99 % CI for π1-π2, the true different in wearing seatbelts between male

and female

c. Is the observed different between male and female significant at the α=0,01 level?

Diketahui :

X1 = 60 X2 = 70

N1 = 100 N2 = 100

α = 0,01 CI = 99%

Jawaban :

P’ = X1 + X2 = 60 + 70 = 130 = 0,65

N1 + N2 100 + 100 200

SE =

= = 0,067

(π1-π2) = (p1-p2) + Z1/2α x SE

= (0,6-0,7) + 2,58 x 0,067

= {-0,27 ; 0,07)…CI 99%

6. A survey of 100 women and 100 man indicated that 49 of the women and 35 of the man

said they were trying to lose weight.

a. Estimate the different in the proportion desiring to lose weight between men and

woman

b. Performed a test of significant to determine whether this different is significant at the

α = 0,05 level

c. Calculate a 95% CI for π1-π2

d. Do the results from (b) and (c) support or contradict each other?Why?

Diketahui :

X1 = 49 X2 = 35

N1 = 100 N2 = 100

α = 0,05 CI = 95%

Jawaban :

- Ho : tidak ada perbedaan proporsi antara keinginan untuk menurunkan berat badan

pada laki-laki dan wanita

Ha : ada perbedaan proporsi antara keinginan untuk menurunkan berat badan pada

laki-laki dan wanita

- α = 0,05

- P’ = X1 + X2 = 49 + 35 = 84 = 0,42

N1 + N2 100+100 200

SE =

= = 0,07

Uji Z

Z = P1-P2

SE

= 0,49 – 0,35 = 2

0,07

Z = 2 = 0,4772

Pv = 0,5 – 0,4772 = 0.0228

Pv < α Ho ditolak

- Ada perbedaan yang signifikan antara proporsi keinginan untuk menurunkan berat

badan pada laki-laki dan wanita

7. A fitness survey found that 35 out of 100 women and 25 out of 100 men did not exercise.

Is this likely to be a real different, or can it be explained by chance? Construct a 95% CI

for the different and state your conclusion.

Diketahui :

X1 = 35 X2= 25

N1 = 100 N2 =100

CI = 95%

Jawaban :

a. Ho : tidak ada perbedaan proporsi berolahraga pada wanita dan laki-laki

Ha : ada perbedaan proporsi berolahraga pada wanita dan laki-laki

b. α = 0,05

c. P’ = X1 + X2 = 35 + 25 = 60 = 0,3

N1 + N2 100 +100 200

SE =

= = 0,065

Uji Z

Z = P1-P2

SE

= 0,35 – 0,25 = 1,53

0,065

Z = 1,53 = 0,4370

Pv = 0,5 – 0,4370 = 0.063

Pv > α Ho gagal ditolak

d. Tidak ada perbedaan yang signifikan antara proporsi berolahraga pada wanita dan

laki-laki

8. A random sample of 100 industrial workers found that 13 of them were exposed to toxic

chemical routinally on their job. Prepare a report that will provide management with

information regarding the magnitude of this problem. What statistic or statistics would

you include in your report?

Diketahui :

X = 13

N = 100

CI = 95%

Jawaban :

SE = = = 0,03

π = p + X1/2α x SE

= 0,13 + 1,96 x 0,03

= {0,07 ; 0,19}…CI 95%