QUESTION 1

Suppose you manage an algorithmic trading operation where computers are trading in the stock market automatically without human intervention using algorithms. Suppose that your algorithm called “Shining Star” (SS) makes an average profit of $6000 each trading hour in the stock market. However, your gut instinct is that the algorithm’s performance has decreased recently. We have provided a random sample of 75 of the more recent hours of trading performance.

PARTS

Write down a hypothesis test for checking if the performance has decreased. Suppose your significance level is 0.01 .

a) Write down the test statistic.

b) What is the name of the model/distribution that would be appropriate to use for the probability distribution of the test statistic? Also, please state your assumptions for picking that distribution.



c) Please provide as much information as you can about the relevant parameters for the distribution (e.g., mean and standard deviation) under the status quo or null.

a) What is your p-value for this test?

b) What is the critical threshold for your test statistic?

b) Has the performance of your SS algorithm decreased? Why or why not?

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a) Now write down a hypothesis test for checking if the performance has increased. Suppose your significance level is 0.01 .

b) What is your p-value for this test?

c) Has the performance of your SS algorithm increased? Why or why not?

QUESTION 2

Internet retailers have so much data!   Epods.com finds that there is a 10% chance that a visitor buys a product. Using sales data over the past two years, you’ve helped them realize that if a visitor spends a long amount of time on the site (i.e., more than 5 minutes), it effects the probability of the visitor buying a product. In particular, among all the buys made by visitors, 80% of time the visitor spent a large amount of time on the site. Among all the visits that resulted in no buy or purchase, 25% of the time the visitor spent a large amount of time on the site.
For all the parts below, if there is a formula involved, please show your work or the relevant formula using probabilistic notation, e.g., P( something1 | something2 ) = … .

Hint:
Define the events

B = visitor buys a product
L = visitor spends a long amount of time on the site (i.e., more than 5 minutes)

What is the prior probability of a visitor buying a product?

What is the conditional probability of a visitor spending a long amount of time on the site, given that the visitor makes a purchase?

What is the conditional probability that a visitor buys a product given that the visitor spends a long amount of time on the site?

What is the conditional probability that a visitor does not make a purchase given that the visitor has spent a long time on the site?

What is the conditional probability that a visitor makes a purchase given that the visitor does not spend a long time on the site?

QUESTION 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.

QUESTION 3

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.

What is the concept of Expenditure Multiplier? Where does it start, and what is the end result (what factors would change in the process)?

Please insert a graph on your paper which shows how the multiplier actually works, and explain step by step of what is happening.

Please fully explain what happens to the multiplier when the aggregate demand is increased in Short Run; and explain what happens whens to the multiplier when the aggregate demand is increased in Long Run. Use the graphs available on your slides and explain step by step.   

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2. What are the signs (red flags) that makes an employer suspect an employee is stealing or causing computer crime?

What is a size of a typical investment management team? Why is employee turnover a “red flag” at an investment firm?

Expected return and standard deviation. Use the following information to answer the​ questions:

a.  What is the expected return of each​ asset?

b.  What is the variance of each​ asset?

c.  What is the standard deviation of each​ asset? ​

State of Economy   Probability of State    Return on Asset A in State   Return on Asset B in State   Return on Asset C in State
Boom 0.31 0.02 0.25 0.31
Normal 0.48 0.02 0.06 0.17
Recession 0.21 0.02 -0.04 -0.24

Hint: Make sure to round all intermediate calculations to at least seven​ (7) decimal places. The input​ instructions, phrases in parenthesis after each answer​ box, only apply for the answers you will type.

Expected return and standard deviation.

Use the following information to answer the questions.

a.  What is the expected return of each​ asset?

b.  What is the variance of each​ asset?

c.  What is the standard deviation of each​ asset?

​Hint: Make sure to round all intermediate calculations to at least seven​ (7) decimal places. The input​ instructions, phrases in parenthesis after each answer​ box, only apply for the answers you will type.

Expected return and standard

deviation.

Use the following information to answer the questions.

a.  What is the expected return of each​ asset?

b.  What is the variance of each​ asset?

c.  What is the standard deviation of each​ asset?

​Hint: Make sure to round all intermediate calculations to at least seven​ (7) decimal places. The input​ instructions, phrases in parenthesis after each answer​ box, only apply for the answers you will type.

Capstone Project: Milestone 2: Design Proposal

Stakeholders

You will be the leader of the team since this is your project. Who will you also include in your team? Make sure you choose relevant stakeholders. You should have no more than eight members. Do not list your team members by name but instead by position (pharmacists, charge nurse, etc.).

Determine Responsibility of Team Members

Why are the members chosen important to your project? What are their roles?

Evidence

Conduct internal/ external search for evidence. What type of evidence did you find in addition to you Evidence Summary? EBP guidelines? Quality improvement data? Position statements? Clinical Practice Guidelines? Briefly discuss the strength of this research. This is not where you describe the results of your studies. This is done in the following steps.

Summarize the Evidence

In this section, you need to synthesize the information from the systematic review article. What are some of the evidence-based interventions you discovered in your Evidence Summary that do you plan to use? Be sure and cite all of your references, in proper APA format, from any and all articles into this one paragraph.

Develop Recommendations for Change Based on Evidence

What is your recommendation based on the research? Ideally, you will have found enough support in your evidence to proceed with implementing your pilot program.

Translation

Action Plan

You have not implemented your project yet, therefore, this section will be hypothetical. Develop your plan for implementation. What are the specific steps you will take to implement your pilot study? What is the timeline for your plan? Make sure you include a plan for evaluation of outcomes and method to report the results.

Process, Outcomes Evaluation and Reporting

What are the desired outcomes? How will they be measured? How will you report the results to the key stakeholders?

Identify Next Steps

How will you implement the plan on a larger scale? Will this be applicable to other units or the facility as a whole? What will you do to ensure that the implementation becomes permanent?

Disseminate Findings

How will you communicate your findings internally (within your organization) and externally (to others outside of your organization)?

Conclusion

Provide a clear and concise summary. Review the key aspects of the problem as well as the change model. Be sure to include important aspects of the five points of the ACE Star change model EBP process and ways to maintain the change plan.

What are natural monopolies? Why do state governments regulate them? What options do state have to regulate them and what are the problems faced by each regulatory option?

1. State the 95% confidence interval for sigma unknown.
2. What is the multiplier used by Excel if sigma is unknown?
3. What do you notice about the 95% Confidence Intervals when sigma is known versus unknown? Explain.