bs1501 tutorial 3_final
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Applied Statistics and Mathematics in Economics & Business
BS1501
Tutorial 3Pairach Piboonrungroj
(Champ)
me@Pairach.com
1. A Yogurt manufacturer
(a)
33,500,5700 xx
017.0)12.2( ZP
33
500570)570( zPxP
x
xzPxxP
0
0 )(
1. A Yogurt manufacturer
(b)
740.0)12924.0(21
x
xzPxxP
0
0 )(
)82.8,500(~~~ xNx
82.8
500510
82.8
500490)510490( ZPxP
)13.1(21)13.113.1( zPZP
nx
82.814
33
Z = -1.13 Z = 1.13
2. Women shift-workers
(a) 04.0150
)40.0)(60.0(60.0)ˆ( pE
n
PPp
)1(ˆ
04.0
60.070.0
04.0
60.060.0()70.0ˆ60.0( ZPPP
4938.00062.05.0)5.20( ZP
04.0
60.050.0)50.0ˆ( ZPPP
9938.00062.01)5.2(1)5.2( ZPZP
(b)
3. A Building Society
(a) n
s*1.645xfor C.I. 90%
30
8500*1.64515200
84.1775216.12667
n
s*2.57xfor C.I. % 99
30
8500*57.215200
33.1918867.11211
n
s*Zxfor C.I.
2
(b)
4. Voters from the electorate
(a)
n
xP ˆ
45.0400
180ˆ P
180 indicated their preference for a particular candidate (x)
400 sample voters (n)
4. Voters from the electorate
(b)
049.045.0
n
)P̂-(1P̂Zˆfor C.I.
2
PP
n
)P̂-(1P̂Zˆfor C.I. % 95
2
05.0PP
400
0.55*0.451.9645.0
499.0401.0 P
4. Voters from the electorate
(c)
064.045.0
n
)P̂-(1P̂Zˆfor C.I.
2
PP
n
)P̂-(1P̂Zˆfor C.I. % 99
2
01.0PP
400
0.55*0.4557.245.0
514.0386.0 P
5. Lifetime of light bulbs
(a)
5.2
100120
16001570
,100n ,1570x 120s
1600:0 H
1600:1 H
nsx
z
01.0
Reject H0 if z < -1.96 or if Z>+1.96
Reject H0 at 5% level of significance
i.e. There is sufficient evidence at 5% level of significance to reject the hypothesis that the mean lifetime of bulbs has changed, but not at the 1% level.
05.0
Reject H0 if z < -2.58 or if Z>+2.58
< -1.96 BUT > -2.58
5. Lifetime of light bulbs
(b)
5.2
100120
16001570
nsx
z,100n ,1570x 120s
1600:0 H
1600:1 H
05.0 01.0
Reject H0 if z < -1.64 (one tailed)Reject H0 if z < -2.33 (one
tailed)
Reject H0 5% and 1% levels of significance.
The first alternative hypothesis would seem to be a fairly weak one compared to the second one, given that it would be of more interest to know whether the mean lifetime of the population of bulbs has deteriorated, rather than simply change.
6. Rent for student room in Cardiff
(a)
220:
220:
1
0
H
H
ns
xz 0
4035
220230
Reject H0 if Z<-1.96 or if Z>1.96.
Thus we do not reject H0, i.e. the claim of
£220 per month cannot be rejected.
=1.81
n
sZx *025.0
40
35*96.1230
85.24015.219
C.I. for
Do not reject H0 since £220 is in the above interval.
(b)
7. A bank manager & her customers
(a)
30.0:
30.0:
1
0
pH
pH 20.0100
20ˆ p
045.0100
70.0*30.0ˆ p
96.122.2045.0
30.020.0ˆ
ˆ
0
P
PPZ
Therefore, we reject at 95% level of confidence.
Reject H0 if Z<-2.57. Thus do not reject H0 at 1% level of significance.
(b)
Thank You for Your Attention
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