Sierra Howard, Kailynn Glenn, Tara Murphy, David Isaac, Xiang Fan
ASSIGNMENT 2
10 POINTS
(1) One of the most controversial issues in the field of Marketing is the long-run impact that
advertising has on brand awareness. That is, while a short-term impact is commonly observed
(i.e. increased awareness of the advertised brand within a one-two week time frame of the ad
appearing), the longer-term impact is less well understood. To this end, the Wharton Marketing
Research Team (WMRT) conducted a study to assess the longer-term impact of advertising on
his newly launched brand of detergent, clean-so-good (CSG). The way WMRT conducted the
study for CSG was as follows:
(i) The WMRT split the population into families without children (FWTC) and families with
children (FWC).
(ii) From each of these two populations WMRT selected a random sample of 50 households
without replacement from phone company records.
(iii) Before any advertising occurred, WMRT asked each of the households to check off from
a provided list of all major brands of detergents (of which CSG is one of them) which brands
they were aware of. (The BEFORE data)
(iv)The results of the BEFORE study indicated that 12 out of 50 FWTC were aware of CSG
while 18 out of 50 FWC were aware.
(v) For a one week period CSG ran a set of national advertisements in all major markets.
(vi)Six months later WMRT collected data in an identical fashion to step (iii), but now AFTER
the advertising campaign.
(vii) The results of the AFTER study, obtained from a new random sample without
replacement from the FWTC and FWC populations indicated that 14 out of 50 FWTC and 28 out
of 50 FWC were aware of CSG.
Based on this information provided, please answer the following questions.
[1a] What type of sampling design (e.g. simple random sampling, cluster sampling, etc…) was
utilized in the study described above? (1 pt)
This study used a stratified sample sampling design.
[1b] Construct 95% confidence intervals for awareness, for FWC and FWTC separately,
BEFORE advertising. (2 pt)
Constructing a 95% confidence interval we find that FWC was at (0.227, 0.493) and FWTC was
at (0.13, 0.37) before advertising.
Sierra Howard, Kailynn Glenn, Tara Murphy, David Isaac, Xiang Fan
Formula:
CI Width= 95% Value of t= 1.96
FWC: p= 18/ 50= 0.36, n= 50
Low end point: = 0.227
High end point: = 0.493
FWTC: p=12/50= 0.25, n=50
Low end point: = 0.13
High end point: = 0.37
[1c] Construct 99% confidence intervals for awareness, for FWC and FWTC separately, AFTER
advertising. (2 pt)
Constructing a 99% confidence interval we find that FWC (0.3792, 0.7408) and FWTC (0.1165,
0.4435) after advertising.
Formula:
CI Width= 99% Value of t= 2.575
FWC: p= 28/ 50= 0.56, n= 50
Low end point: = 0.3792
High end point: = 0.7408
FWTC: p=14/50= 0.28, n=50
Low end point: = 0.1165
High end point: = 0.4435
Sierra Howard, Kailynn Glenn, Tara Murphy, David Isaac, Xiang Fan
[1d] Provide test statistics and p-values, for both the FWTC and FWC groups, that the fraction of
people who were aware of CSG BEFORE the advertising is the same as the fraction of people
AFTER the advertising, versus the alternative that advertising increased the awareness. (1 pt)
(Insert screenshot of excel)
=0.0714+0.051+0.1264+0
.0902
=0.339
(2) One further question of interest to WMRT is whether the number of times that some saw the
advertisement (if at all) is related to the long-run impact of the advertisement on awareness. To
assess this, WMRT collected data on how many times CSG’s ad was seen and whether or not the
household was aware of the advertisement six months later after the campaign had ended. The
data from this study can be summarized in the following table from a random sample of 850
potential customers.
Was Aware of
CSG
Not Aware of
CSG
Did not see the advertisement 80 120
Saw the advertisement between 1-3
times 140 150
Saw the advertisement more than 3
times 220 140
Based on the information in this table, answer the following questions.
(2a) What proportion of customers saw the advertisement at least once? (1 pt)
650
850
= 0.76
(2b) Given that someone is aware of CSG, what is the probability that they did not see the
advertisement? (1 pt)
Sierra Howard, Kailynn Glenn, Tara Murphy, David Isaac, Xiang Fan
80
440
= 0.18
(2c) Construct a 99% confidence interval for the proportion of households that are aware of
CSG. (1 pt)
low-end point:
440
850
- (2.575)*(
√
(440
850 )∗( 410
850 )
850
) = 0.473
high-end point:
440
850
+ (2.575)*(
√
(440
850 )∗( 410
850 )
850
) = 0.562
(0.473, 0.562)
(2d) Test whether the number of times that a household saw the advertisement is independent of
whether or not they are aware of CSG. (Provide the relevant test statistic and p-value.) What
might this result indicate about the long-term effect of advertising, if anything? (1 pt)
p-value: 0.00000355
test statistic: 25.1
With a p-value of 0.00000355, this demonstrates that the number of times a household saw the
advertisement was independent from whether or not they were aware of CSG.
actual
Was Aware of CSG Not Aware of CSG total
Did not see the advertisement 80 120 200
Saw the advertisement between 1-3 times 140 150 290
Saw the advertisement more than 3 times 220 140 360
total 440 410 850
expected
103.5 96.5 200.0
150 140 290
186 174 360
440.0 410.0 850.0
=CHISQ.TEST(insert actual range, insert expected range) = 0.00000355
