UESTION 3 and QUESTION 4: Context
Suppose you are part of the analytics team for the online retailer Macha Bucks which sells two types of tea to its online visitors: Rouge Roma (RR) and Emerald Earl (EE). Everyday approximately 10,000 people visit the site over a 24 hour period. For simplicity suppose we consider the “buy one or don’t buy” (BODB) market segment of customers which when they visit the site will conduct one of the following actions: (a) buy one order of RR, (b) buy one order of EE, or (c) don’t buy (DB) anything. You have been tasked with determining customer behavior on the website for the BODB segment using a random sample of 35 visits.
In the dataset for the random sample, each row corresponds to a random visitor. For each visitor we provide both the visitor’s action as well as the profit earned on the transaction. In the action column:
if the visitor buys one order of RR, we see a RR,
if the visitor buys one order of EE, we see an EE,
if the visitor doesn’t buy anything, we see a DB.
Note that even if two customers buy the same product, the profit can differ due to the shipping costs, promotions, or coupons that are applied
Random Sample of Data
1=yes, 0 = no
Transaction ID
Action
Profit ($)
Bought RR?
Bought EE?
Didn't Buy?
Profit RR ($)
Profit EE ($)
1
RR
8.43
1
0
0
.
0.00
2
DB
0.00
0
0
1
0.00
0.00
3
EE
1.75
0
1
0
0.00
1.75
4
DB
0.00
0
0
1
0.00
0.00
5
EE
4.37
0
1
0
0.00
4.37
6
EE
5.79
0
1
0
0.00
5.79
7
RR
6.27
1
0
0
6.27
0.00
8
RR
6.22
1
0
0
6.22
0.00
9
DB
0.00
0
0
1
0.00
0.00
10
EE
4.49
0
1
0
0.00
4.49
11
RR
10.54
1
0
0
10.54
0.00
12
EE
3.79
0
1
0
0.00
3.79
13
DB
0.00
0
0
1
0.00
0.00
14
DB
0.00
0
0
1
0.00
0.00
15
RR
9.03
1
0
0
9.03
0.00
16
EE
3.54
0
1
0
0.00
3.54
17
DB
0.00
0
0
1
0.00
0.00
18
DB
0.00
0
0
1
0.00
0.00
19
EE
5.02
0
1
0
0.00
5.02
20
DB
0.00
0
0
1
0.00
0.00
21
EE
3.60
0
1
0
0.00
3.60
22
DB
0.00
0
0
1
0.00
0.00
23
EE
2.61
0
1
0
0.00
2.61
24
RR
11.75
1
0
0
11.75
0.00
25
RR
12.22
1
0
0
12.22
0.00
26
DB
0.00
0
0
1
0.00
0.00
27
DB
0.00
0
0
1
0.00
0.00
28
EE
6.17
0
1
0
0.00
6.17
29
RR
8.83
1
0
0
8.83
0.00
30
DB
0.00
0
0
1
0.00
0.00
31
DB
0.00
0
0
1
0.00
0.00
32
DB
0.00
0
0
1
0.00
0.00
33
DB
0.00
0
0
1
0.00
0.00
34
RR
14.16
1
0
0
14.16
0.00
35
EE
6.06
0
1
0
0.00
6.06
PARTS
Using the sample data, obtain a point estimate for the proportion
of customers in this BODB market segment that
a) purchase EE:
b) purchase RR:
c) don’t buy:
a) What is the name of the model/distribution that would be
appropriate to use for the probability distribution of the sample
proportion of the BODB market segment that purchases EE?
b) Please provide as much information as you can about the relevant
parameters for the distribution (e.g., mean and standard
deviation).
Please provide a 95% confidence interval for population proportion
of the BODB market segment that
a) purchase EE:
b) purchase RR:
c) don’t buy:
a) What does the 95% confidence interval mean intuitively? Please
provide an interpretation.
b) What could you do to obtain a narrower 95% confidence
interval?
c) What would you need to do to have a margin of error of 0.05?
Please do the calculation.
a) Please provide a 99% confidence interval for the population
proportion of the BODB market segment that purchases EE.
b) When would you prefer a 99% confidence interval rather than a
95% confidence interval?
What is the 95% confidence interval for the average profit from
a
a) EE customer (i.e., a customer in the BODB market segment that
buys EE):
b) RR customer (i.e., a customer in the BODB market segment that
buys RR):
c) Clearly state any assumptions you make about the sampling
distribution.
QUESTION 4
PARTS
a) What could be an appropriate probability distribution to use for
modeling the number of visitors that the website has in an
hour?
b) What parameters would you use for the probability
distribution?
c) Using that distribution, determine the probability that more
than 600 people visit the site in an hour.
a) What could be an appropriate probability distribution to use for
modeling the number of seconds between customer visits?
b) What parameters would you use for the probability
distribution?
c) Using that distribution, determine the probability that the time
between customer visits to the website is less than 10 seconds.
a) What could be an appropriate probability distribution to use for
modeling the number of website visitors from 100 visitors that do
not buy anything?
b) What parameters would you use for the probability
distribution?
c) Using that distribution, determine the probability that from
among 100 customers, it turns out that 30 or more customers do not
buy anything.
d) What is the average number of visitors (from among 100
customers) that do not buy anything?
e) What is the standard deviation of the number of visitors (from among 100 customers) that do not buy anything?
What is the average profit from among 100 random customers that
visit the site?
Please explain your answer or show your calculations.
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