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250
Chapter 14
14.1 Equalvariances ttest of 2 1 m  m
0 ) ( : 2 1 0 = m  m H
0 ) ( : 2 1 1 < m  m H
÷ ÷ø
ö
ç çè
æ
+
m  m  
=
2 1
2
2 1 2 1
1 1
) ( ) (
n n
s
x x
t
p
t = 5.09, pvalue = 0. There is overwhelming evidence to conclude that there has
been a decrease
over the past three years.
14.2 a ztest of 2 1 p p  (case 1)
0 ) ( : 2 1 0 =  p p H
0 ) ( : 2 1 1 >  p p H
÷ ÷ø
ö
ç çè
æ
+ 

=
2 1
2 1
1 1
) & 1 ( ±
) G “ (
n n
p p
p p
z
tTest: TwoSample Assuming Equal Variances
This Year 3 Years Ago
Mean 8.29 10.36
Variance 8.13 8.43
Observations 100 100
Pooled Variance 8.28
Hypothesized Mean Difference 0
df 198
t Stat 5.09
P(T<=t) onetail 0.0000
t Critical onetail 1.6526
P(T<=t) twotail 0.0000
t Critical twotail 1.9720
251
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View Full Document z = 2.83, pvalue = .0024. There is overwhelming evidence to infer that customers
who see the ad are
more likely to make a purchase than those who do not see the ad.
b Equalvariances ttest of 2 1 m  m
0 ) ( : 2 1 0 = m  m H
0 ) ( : 2 1 1 > m  m H
÷ ÷ø
ö
ç çè
æ
+
m  m  
=
2 1
2
2 1 2 1
1 1
) ( ) (
n n
s
x x
t
p
t = .90, pvalue = .1853. There is not enough evidence to infer that customers who
see the ad and
make a purchase spend more than those who do not see the ad and make a purchase.
c zestimator of p
n
p p
z p
) & 1 ( ±
X 2 /

² a
zTest of the Difference Between Two Proportions (Case 1)
Sample 1 Sample 2 z Stat 2.83
Sample proportion 0.4336 0.2414 P(Z<=z) onetail 0.0024
Sample size 113 87 z Critical onetail 1.6449
Alpha 0.05 P(Z<=z) twotail 0.0047
z Critical twotail 1.9600
tTest: TwoSample Assuming Equal Variances
Ad No Ad
Mean 97.38 92.01
Variance 621.97 283.26
Observations 49 21
Pooled Variance 522.35
Hypothesized Mean Difference 0
df 68
t Stat 0.90
P(T<=t) onetail 0.1853
t Critical onetail 1.6676
P(T<=t) twotail 0.3705
t Critical twotail 1.9955
252
We estimate that between 34.23% and 52.50% of all customers who see the ad will
make a purchase.
d testimator of m
n
s
t x 2 / a ±
We estimate that the mean amount spent by customers who see the ad and make a
purchase lies
between $90.22 and $104.55.
14.3 ttest of D m
0 : 0 = mD H
0 : 1 > m D H
D D
D D
n s
x
t
/
m 
=
t = .70, pvalue = .2438. There is not enough evidence to conclude that the
equipment is effective.
tTest: Paired Two Sample for Means
Before After
Mean 381.00 373.12
Variance 39001.33 40663.28
Observations 25 25
Pearson Correlation 0.9610
Hypothesized Mean Difference 0
df 24
t Stat 0.70
P(T<=t) onetail 0.2438
t Critical onetail 1.7109
P(T<=t) twotail 0.4876
t Critical twotail 2.0639
zEstimate of a Proportion
Sample proportion 0.4336 Confidence Interval Estimate
Sample size 113 0.4336 0.0914
Confidence level 0.95 Lower confidence limit 0.3423
Upper confidence limit 0.5250
±
tEstimate: Mean
Ad
Mean 97.38
Standard Deviation 24.94
LCL 90.22
UCL 104.55
253
14.4 a ztest of p
: 0 H p = .95
: 1 H p > .95
n
p p
p p
z
) 1 (
5


=
z = 1.54, pvalue = .0619. There is not enough evidence to infer that the
spokesperson's claim is true.
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This note was uploaded on 06/06/2011 for the course ADMS 2320 taught by Professor Rochon during the Spring '08 term at York University.
 Spring '08
 ROCHON

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