Tag Archives: data

Solution to Management Science Series #216: Should Condor launch a new website?

An online video games store named ‘Condor’ needs to test its old and new web designs. Condor randomly redirects a sample of customers to either site and measures the sales information of customers who purchase.

Condor will launch the new website only if it is 90% confident that the new site generates more sales per transaction (i.e. average transaction amount) than the old website.

Below are shared the data for the sample of customer transaction amounts from the new site and that from the old site.

a) Could you make an educated guess on what Condor should do without calculating anything?

b) Design a hypothesis test and determine whether Condor should roll out the new website.

c) Solve the same problem by using Excel.

Solution to Management Science Series #215:Real-world example: Cornell Endowment

Selim Hasagasioglu Academy and Consulting Services agreed with Cornell University’s Office of University Investments on increasing the average donation per Cornellian including alumni and current students.

Last year, average donation value was $200 per Cornellian. Selim’s company designed a new digital donation platform and was additionally tasked with assessing whether the new platform increases the average donation amount. The company investigated a random sample of 60 disparate donations and the sample’s average was calculated as $225 while the sample standard deviation was $100.

a. Help the company construct the Null and Alternative Hypotheses.
b. At a significance level of α=0.05, what should Cornell do, considering the results of this marketing experiment?
c. What kind of information is provided through this hypothesis testing project?

Solution to Management Science Series #214: Real-world example: Berserk Toy Company improving its QC processes

Berserk Toy Figures is a toy company producing its copyrighted Guts figures.

The manufacturing process owned by the company creates the head part of the figure that is designed to be 19 mm wide with a standard deviation of 1.5 mm.

Head part of the figure is an important feature of the figure and regularly goes through the Quality Control. QC sample size is 35 parts. A recent batch of head parts appeared to have an average width of 18mm.

1.What is the probability of getting an average width equal to or less than 18mm?

2. Is there a quality problem? Use your finding in 1.

3. Berserk Toys is a boutique toy maker that could not afford to stop production and run a root cause analysis. How can the company tackle this problem and increase the confidence?

Solution to Management Science Series #213: Real-world example: Marbella Call Center

Marbella Call Center is a contractor assessing the quality of calls to the customer services of top global brands. Recently, Marbella agreed with Eldorado, a global retailer, on assessing the quality of the customer service of Eldorado.

Marbella has been periodically recording a random sample of customer calls to Eldorado. Calls are evaluated on whether the employee taking the call abides by Eldorado’s customer support policies.

Historically, 80% of all calls conformed to the policy. A recent sample of 120 calls found that 70 adhered to the policy.

1. What is the sample proportion?

2. Is the normal distribution a good approximation?

3. What is the expected value and standard deviation of the sample proportion?

4. What is the probability of getting 70 or fewer calls that adhered to the company policy?

5. Do you see any problems concerning the adherence to the company’s customer support policies?

Solution to Management Science Series #212: Real-world example: Determining Portfolio Returns

An ETF created by the investment management firm, Gold Returns (GR) has a normally distributed expected monthly return with μ = 2% and σ = 8%.

a)What is the probability that the return is positive next month?

b)What is the probability that the portfolio’s return exceeds 10%?

c)What is the median return?

d)What is the first quartile of return?

Solution to Management Science Series #211: Real-world example: Kabuto Drinks forecasting production capacity and launching a loyalty program

A soft-drink company called Kabuto plans to model the production capacity for the year 2026.

The forecasters determined that the annual soft-drink consumption with the respect to Kabuto’s brands is normally distributed with a mean of 160 liters per customer of Kabuto per year and a standard deviation of 40 liters per customer per year.

a)What is the median per person annual consumption?

b)What is the mode for the per person annual consumption?

c)What percentage of Kabuto consumers do consume more than 160 liters per year?

d)What percentage of Kabuto consumers do consume more than 200 liters per year?

e)What percentage of Kabuto consumers do consume more than 230 liters per year?

f)What percentage of Kabuto consumers do consume fewer than 120 liters per year?

g)Your marketing department is proposing a loyalty program for the consumers who lie within the top 5% of Kabuto-branded soft-drink consumption. Find the threshold value of annual Kabuto drink consumption for these top consumers in liters.

h)In an alternative scenario, Kabuto will have customers within the top 3% of consumption join the loyalty program. Find the threshold value of annual Kabuto drink consumption for these top consumers in liters.

Solution to Management Science Series #210: Real-world example: Famous hotel chain, Mushroom Kingdom, bent on improving customer satisfaction

Real-world example: Famous hotel chain, Mushroom Kingdom, bent on improving customer satisfaction

You are the owner of the famous hotel chains called Mushroom Kingdom (MK). Historically, 75% of all the customers claimed that they were ‘completely satisfied’ with the services and accommodation offered by the MK.

You hired an analytics company, named Gotham Analytics (GA), that would conduct analyses to determine whether this still holds true. GA conducted a survey, by randomly sampling 35 customers out of a total of chain’s 250 customers. The number of customers in the sample who claimed that they were ‘completely satisfied’ is 25.

1) Calculate the sample proportion.

2) Could you assume that the distribution of the sample proportion is normal?

3) What is the standard deviation of the sample proportion using the finite population correction factor?

4) What is the standard deviation of the sample proportion ignoring the finite population correction factor?

5) Recalculate 3) and 4) assuming the chain has 110 customers.

6) Recalculate 3) and 4) assuming the chain has 1500 customers.

7) Assume again that the firm has 250 customers. Using the finite population correction factor to calculate the standard deviation of the sample proportion, what is the likelihood of finding 25 or fewer “completely satisfied” customers in a sample of 35 customers?

Solution to Management Science Series #209: Mysterious Disease in a Tropical Island: Data Analytics & Medicine

Mysterious Disease in a Tropical Island: Data Analytics & Medicine

23% of males in the tropical island, Cappytopa, are known to carry a mysterious disease called ‘Dinosaur flu’.

A newly developed test correctly detects dinosaur flu 90% of the time for males, but incorrectly detects dinosaur flu in non-infected males 35% of the time (false positive).

1.A randomly selected male is tested for the dinosaur flu and the result is positive. What is the probability that this male is dinosaur flu positive?

2.What is the probability that this same male is dinosaur flu negative?

3.What is the probability that a randomly selected male has a positive test? Would you trust in this test?

Solution to Management Science Series #208: Zodd Japanese Manga trying to improve customer satisfaction

Selim Hasagasioglu Academy and Consulting Services was contacted by a very niche e-commerce platform called Zodd that markets and sells Japanese manga and relevant merchandise.

Zodd has been recently struggling with customer satisfaction issues. Furthermore, Zodd does not have the information on the historical customer satisfaction levels.

Selim’s firm carried out a survey, randomly sampling 50 customers out of the firm’s 1300 customers. The number of customers in the sample who claimed that they were ‘entirely satisfied’ was 35.

a) Do you need to use the finite population correction factor?

b) What is the sample proportion for the sample collected by Selim’s firm?

c)Is the distribution of the sample proportion normal or can it be used to conduct a confidence interval analysis?

d) What is the margin of error assuming a 95% confidence level?

e) What is the 95% confidence interval for the proportion of customers who are “entirely satisfied”? What is the 99% confidence interval? Are you 95% confident that customers are more than likely to be entirely satisfied with Zodd? Are you 99% confident that customers are more than likely to be entirely satisfied with Zodd?

f) How many customers should be sampled to ensure a margin of error of 0.12 with a 90% confidence level if you use p* = 0.5?

g) How many customers should be sampled to ensure a margin of error of 0.12 with a 90% confidence level if you use p* = 0.75?

h) Between the answers to f) and g), which is a more conservative approach and why is this difference important in the practice of data/business analytics?

Solution to Management Science Series #207: Marketing real-world example ‘Crenner Toys designing a promotion’

Marketing real-world example: Crenner Toys designing a promotion

Crenner Toys, famous for its toy vehicles transforming into attack vehicles and sold with complementary figures, is planning to roll out a promotion through which Crenner will send discount codes to its existing customers via emails.

Crenner will deem this promotion viable and subsequently implement it at national scale only if more than 15% of customers receiving the codes use them within 10 days. To assess the viability of this promotion, Crenner sent codes to a random sample of 150 customers and 23 of those receiving the code used it.

1.Construct the Null and Alternative hypotheses.

2.Should Crenner launch this promotion at national scale? Crenner believes that a significance level of 5% is appropriate for the hypothesis testing.