Advanced Data Analytics – Selim Hasagasioglu

Solution to Management Science Series #220: Another real-world example: Average time spent on childcare by fathers of Arkham Island

Average time spent on childcare by fathers of Arkham Island

A recent study claims that the time fathers spend on childcare is 7.1 hours per week. Drawing on this survey, your company needs to prove true that the time fathers living on the Arkham Island spend on childcare per week differs from that value. Your company, ‘Wizard Statistics’, sampled 50 fathers and recorded the number of hours per week spent on childcare. The sample information is shared in the accompanying Excel worksheet.

a)Using hypothesis testing, determine whether the time fathers living on the Arkham Island spend on childcare per week differs from 7.1 hours per week. Use significance levels of 5% and 10%. Solve the problem manually.

b) Solve the same problem, using Excel.

Solution to Management Science Series #219: Another real-world example: Tindendo considering changing its suppliers

Tindendo is a famous video game console manufacturer based in Kagoshima, Japan. Tindendo uses a very specific chip for its consoles currently in the market. However, Tindendo plans to research other possible suppliers that could provide these chips at least in the same quality as that ensured by the incumbent supplier.

To that end, Tindendo has found an alternative supplier. Tindendo randomly sampled 50 parts from both the incumbent and the alternative supplier and came up with a methodology and proprietary technology that could measure by how much each part deviates from the required specification.

Although switching costs are high for this particular part, Tindendo determined that they could work with the alternative supplier if the average deviation from the standard required measures for the incumbent supplier were to be 5 nanometers or higher than that for the alternative supplier.

The average variation for the samples supplied by the incumbent supplier is 54 nanometers with a standard deviation of 9 nanometers. The average variation for the samples supplied by the alternative supplier is 48 nanometers with a standard deviation of 7 nanometers.

a) Should Tindendo change its supplier if it were to use a level of significance of 5%?

b) Assume that Tindendo determined that it could work with the alternative supplier if the average deviation from the standard required measures for the incumbent supplier were to be 2 nanometers or higher than that for the alternative supplier. Should Tindendo change its supplier if it were to use a level of significance of 5%?

c) Assume that Tindendo decided to change suppliers provided that the average variation amount for the incumbent supplier is higher than that for the alternative supplier by any amount. Without calculating anything algebraically, could you determine what Tindendo should do in that case (all other inputs values stay the same)?

Solution to Management Science Series #218: Real world example: Interactive Investors Asset Trading Platform

Interactive Investors Asset Trading Platform

Interactive Investors is a well-known asset trading platform used by the citizens of Eldorado. The company plans to improve the platform by adding a feature that would expedite the transaction times.

The company randomly sampled 64 trades and had the new improved platform used for all these transactions. The average transaction time is found to be 25 milliseconds with a standard deviation of 4 milliseconds.

1. Establish the null and alternative hypotheses if Interactive Investors wants to prove whether the average transaction time is different from 28 milliseconds (the average transaction time prior to the change)?

2. Establish the null and alternative hypotheses if Interactive Investors wants to demonstrate whether the average transaction time is less than 28 milliseconds.

3. What should Interactive Investors do if it were to use a level of significance (α) of 0.01 in question 1.

4. What should Interactive Investors do if it were to use a level of significance (α) of 0.01 in question 2.

5. Determine the critical values of the sample mean both of which will cause the alternative hypothesis to be accepted in 1. Use a level of significance (α) of 0.01.

6. Determine the critical value of the sample mean which will cause the alternative hypothesis to be accepted in 2. Use a level of significance (α) of 0.01.

7. How could Type I and Type II errors happen in the context of this problem?

Solution to Management Science Series #217: Real world example: Mushroom Kingdom Social Network

Serra, a video game and console collector, plans to launch a digital forum, which would resemble a social network only for people who collect video games and consoles.

She wants to name it ‘Mushroom Kingdom Social Network’. Albeit optimistic about the prospects of this new venture, Serra still wants to test whether it is a viable business proposition.

So, she randomly samples 50 collectors and asks them how much time each day they would spend on such a social network. The average value measured through this sample is 53 minutes and the standard deviation is calculated as 23 minutes.

a) State the null and alternative hypotheses if Serra wants to demonstrate whether the amount of time spent on this platform is different from 45 minutes per day.

b) Construct the null and alternative hypotheses if Serra wants to test whether the average amount of time spent on the proposed network is more than 45 minutes per day.

c)What should Serra do if she tests the hypotheses laid out in a), requiring a level of significance of 0.05?

d)What should Serra do if she tests the hypotheses laid out in b), requiring a level of significance of 0.05?

e) Which pair of hypotheses are more conservative, a) or b)?

Now, Serra decides to sample only 40 people randomly.

f)What should Serra do if she tests the hypotheses laid out in a), requiring a level of significance of 0.05?

g)What should Serra do if she tests the hypotheses laid out in b), requiring a level of significance of 0.05?

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.