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Number Analysis in Soft Switch, MSOFT3000.
Number System- Tough Questions
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Assignment Number 2 GENERALIZING FROM THE SAMPLE TO THE POPULATION Alyana ee E! ig"r MPM 2#$%&$ 'ate Submitte( ) %*2+*2#$, 1.
The avera average ge systo systolic lic pres pressur suree of a group group of 36 36 male male student studentss of appro approxim ximatel ately y the same same ages ages is 127.5 If the mean systolic systolic pressure of the population of males of approximately the same ages is 126.5 with a standard deviation of 5 would you say that the 36 male students have a higher systolic pressure than than 126.5! "how the different steps from hypothesis testing to conclusion. (15 points)
f. Since z value is 1.! there is no sufficient evidence to reject
2.
H o
Two group groupss of stud studen ents ts with with 5# mem mem$er $erss each each were were taug taught ht with with diff differ eren entt method methods. s. %rou %roup p1 was taught $y method & while %roup 2 was taught $y method '. The mean scores for %roup 1 was 77 while while for %roup 2 was (5. The standa standard rd deviatio deviation n is 1# for $oth groups. groups. )an the difference in the mean score significant! "how the different steps from hypothesis testing to conclusion. (5 points) a.
H o : Thereis Thereis no signific significant ant differ differencebetwe encebetweed ed method method A ∧ B
H 1 : Thereis significant difference betweed method A ∧ B
b.
α =0.05
√ ´+¿− ´ 2
2
s 1
c.
s2
n1 n2 x 1 x 2
t =
¿
d. Reject
e.
√
10 50
H o
+¿ t =
10 50 77
if computed value of
¿ ± 1.9845 " df =( 50−1 ) + ( 50−1 )=98
= ± 12.65 −85 ¿
f. Since the computed value is more than
± 1.9845
" #here is significant difference
bet$een method % and &.
3.
*etermine whether+ a, there is a relationship and the direction of the relationship $etween &lcohol consumption and date rate from cirrhosis using the data $elow. (15 points) and b) -hat would $e the death rate from cirrhosis for a country with alcohol consumption of 11 liters per person per year! (1' points)
*eath rate from )irrhosis xy per liters per death 1##### person/year, population, 2.7 6.1 1138. &lcohol )onsumption
)ountry
0rance Italy
15.2
%ermany
12.3
&ustralia
1#.
'elgium "&
1#.( .
67 23.6 358.7 2 23.7 291.5 1 7
76.3 12.3 132.8 4 1.2 140.5
x squar ed
y squar ed
610.0 9 231.0 4 151.2 9 118.8 1 116.6 4 98.01
2125. 21 556.9 6 561.6 9 49 151.2 9 201.6
)anada 4ngland "weden apan etherland s Ireland orway 0inland 4ritrea Total
H o : Thereis no relationship betweenalcohol consumption ∧ deathrate ¿ cirrhosis
H 1 : There is relationshipbetween alcoholconsumption ∧deathrate ¿ cirrhosis
xy x
∑¿ ¿
y
∑¿ ¿ ¿ ¿
x
2
∑¿ ¿
x
∑¿ ¿ ¿ ¿
2
2
y y
∑¿
¿ ¿ ¿ ¿ ∑ ¿−¿ ¿ n¿ ∑ ¿−¿ n¿ r =¿ 2
t =
r √ n −2
√ 1−r
2
=
0.9388 √ 15
−2 =9.83 √ 1−( 0.9388 ) 2
α =0.05 ; df =15−2 = 13 ; @ 0.514
" reject null hpothesis if absolute amount is greater
than t table value Since *., is greater than '.51-" $e can reject the null hpothesis and conclude that there is a relationship bet$een %lcohol consumption and death rate from cirrhosis! and has direct or positive relationship" thus an increase in alcohol consumption $ill also increase death rate from cirrhosis. &.
(∑ y )( ∑ x )−(∑ x ) (∑ xy ) (175.5 ) ( 1630.12 )−( 134.2 ) (2419.61 ) a= = =−6.00 ( ) 1 5 1630.12 134.2 − n ( ∑ x )−( ∑ x ) 2
2
b=
n(
2
2
∑ xy )−(∑ x )( ∑ y ) = 15 ( 2419.61 )−( 134.2 ) (175.5) =1.98 15 ( 1630.12 ) −134.2 n ( ∑ x )−( ∑ x ) 2
2
2
y =bx + A =1.98 (11 )−6 =15.78 -. sing the data $elow determine whether people who sleep for four hours will score significantly lower than people who sleep for eight hours on a cognitive sill test. (15 points)
um$er
8ean
"tandard deviation
-ith sleep
(
hours (
5
.57
-ith sleep
hours (
6.57
a. H o : Thereis no significant difference ∈ score for people who sleep for 4 hours
¿ thosewho sleep for 8 hourson a cognitie test H 1 : Thereis significant difference ∈ score for people who sleep for 4 hours
¿ those who sleep for 8 hours on a cognitie test
b. .
α =0.05
c. Reject
H o
if the computed value is greater than .1-5" df +/1-
√
4.57
d.
8
√
+¿
2
s 1
6.57 8
= 0.85
2
s 2
5− 4 = ¿ n n x ´ − x´ t = ¿
+¿
1
2
1
2
e. #here is no further evidence to reject
5.
H o
sing the data $elow can you conclude that there is a significant relationship $etween watching violent television shows and overt aggression on the part of young male viewers. (15 points). *id not )ommitted commit TOTAL aggressive aggressive acts acts
a.
9referred violent television programs
5#
15
65
9referred non:violent television programs
1#
25
35
TOTAL
60
40
100
H o : Thereis no significant differencebetween watching iolent teleision shows
¿ oert aggression on the part of young male iewers H 1 : Thereis significant difference betweenwatching iolent teleisionshows
¿ oert aggressionon the part of young male iewers b.
α =0.05 ; two tailed test
c. x
2
=∑
2
( fo−fe ) fe
chi/s0uare test
d. Reject
H o
if computed value is greater than ,.- "
df =( 2−1 ) ( 2−1 )=1
e. 1st categor
fe 1 =60
( )=
fe 2 =60
( )=
65
100
35
100
2
39 ;
( fo− fe)
2
=
fe 2
21 ;
( fo−fe )
=3.10
39
2
=
fe
(50 −39)
(10− 21)
=5.76
21
nd categor
fe 3 =40
( )=
fe 2 =40
( )=
65
100
35
100
2
26 ;
( fo −fe ) fe
2
=
2
14 ;
( fo−fe ) fe
(15−26 )
= 4.65
26
2
=
( 25−14 ) 14
= 8.64
2
x =3.10 + 5.76 + 4.65 + 8.64 =22.15
f. Since
x
2
is greater than ,.- $e can conclude that there is significant difference
bet$een $atching violent television sho$s and overt aggression on the part of oung male vie$ers.
6.
sing the 2#11 'era;ia data what proportion of the population as a whole in 2#11 would you expect to have hostility scores higher than 2! (5 points)
