Reference no: EM132831654

Question One
There are five key stages of development for a vaccine which are monitored on www.covid- 19vaccinetracker.org. Three of the stages refer to different clinical phases (I, II and III), a Regulatory and Review stage (RR) and finally an authorisation stage (AU). Figure Q1 is a picture of the website www.covid-19vaccinetracker.org taken on February 16, 2021.

Figure Q1 www.covid-19vaccinetracker.org

Identify and briefly describe two key messages from Figure Q1.

Describe one strength and one weakness of the diagram used in Figures Q1.

Propose an alternative graphic from this data to address the weakness you identified in part b).

Question Two
The Ministry of Health is in the process setting up vaccination sites to vaccinate against a highly contagious viral disease. They have hired you as a consultant to help with setting up the supply chain and to help decide on which vaccine among a few existing options is the most effective.

You have been placed in charge of a new vaccination site. Analysts have also provided you with statistics (means and standard deviations) about how other vaccination sites that have been running for a few weeks are performing. These sites are similar to the one you are in charge of in terms of population size and characteristics. The analysts told you that the number of patients that you should expect to arrive each day to get vaccinated is normally distributed with a mean 530 and a standard deviation of 125. The analysts are excellent data scientists and you are certain their estimates are corrects.

The vaccine the site is planning to use is no longer effective after a day out of extreme cold temperatures, and the site does not have freezers that are cold enough. Wasting vaccine doses is a very bad outcome since there is limited supply. On the other hand, you do not want individuals to turn up at appointments and not have doses available to vaccinate them. It is your job to decide how many vaccines the site should receive per day from the central hub, which has freezers that maintain the vaccine's efficacy.

As noted, you have received the mean and standard deviation of the number of patients seeking vaccination every day from the analysts. You have not received the data the mean and standard deviation are based on. If your aim is to make predictions about how many vaccine doses will be wasted each day, would you use the information you were given and the normal distribution to make predictions or would you ask for the full data and make empirical predictions? Explain (points will only be given for valid explanations and not for yes/no answers).

If you order 530 doses per day, what is the probability that you will manage to vaccinate everyone that arrives in a day?

Your assistant suggested your order 800 doses per a day, arguing that you do not want to run into a situation in which someone comes to get vaccinated but you have to turn them away since you have run out of vaccine doses.

What is the probability that you are unable to cover everyone in a random day if you follow your assistant's suggestion?

If you take your assistant's suggestions, what is the probability that not enough people show up and you have to waste at least 10% of the doses you ordered on a random day?

Since you have been doing a good job eliminating vaccine wastage, you have been asked to run 50 vaccination sites, including the one you previously managed. You can assume the distribution of expected patients arriving for vaccination on a random day in each is similarly characterized by a mean 530 and standard deviation of 125.

How many doses per day per site should you order if you want your expected vaccine wastage to be 3%?

Calculate a 95% confidence interval of the mean number of people that will show up to get vaccinated at a vaccination site.

You are asked to advise on which vaccine should be used in the vaccination sites. Vaccine 1's effectiveness protecting against death is 90% (95% Confidence Interval [CI] 82% - 98%), and its effectiveness protecting against disease is 75% (95% CI 60% - 90%). Vaccine 2's effectiveness protecting against death is 81% (95% CI 78% - 84%), and its effectiveness protecting against disease is 58% (95% CI 51% - 65%).

Which vaccine (among Vaccine 1 and Vaccine 2) has better effectiveness protecting against death and which has better effectiveness protecting against disease? What is your recommendation?

Question Three
A local small business has been actively advertising on social media since it was created several years ago. Social media is the business's main form of advertising. The owner is now hoping to be able to better forecast future sales based on social media advertising for two of her main products in order to create an improved production plan and better maintain her inventory. The owner hopes a regression model might also help inform decisions about future social media campaigns. The owner would like your help conducting and interpreting a regression analysis to provide appropriate forecasts.

Some preliminary analysis has been conducted and is provided in the form of Excel output on the following pages. Specifically Figures 3a and 3b are scatter diagrams showing the relationship between advertising and sales for both products. A regression analysis was conducted for product A and is provided in Figure 3c and for product B provided in Figure 3d. Residual plots for the regressions are provided in Figures 3e and 3f.

VARIABLE DESCRIPTIONS:

Month = The month the data was collected (note, months are labelled 1-24, with 1 being the earliest month in the data and 24 being the most recent)
Advertising = the amount spent in one month on social media campaigns, in GBP Product A = the number of units sold of product A that month
Product B = the number of units sold of product B that month

Use the Excel output provided to conduct appropriate analysis to answer the following questions. Include any key statistics you think are appropriate to support your analysis.

Comment on the patterns in the relationships between number of units sold and the amount spent on social media advertising for both products A and B.

What is the correlation between social media advertising and sales of each product? Are these correlations statistically significant? Show your workings and explain your reasoning.

Write down two regression models using advertising to predict sales of each product A and B. Interpret the two models in terms the business owner will understand. Provide the business owner with point and interval estimates forecasting sales in a month with £1500 social media advertising for each of products A and B?

Evaluate the fit of the two regression models, including interpreting and explaining the coefficient of determination (R2), relevant confident intervals, and the residual plots for both models. Explain what these checks mean in terms useful for the business owner.

Which, if any, of the models created might be useful for the business owner to use to forecast sales based on future social media advertising spending? Explain your reasoning to the business owner. What other factors might the owner consider collecting data on in the future to incorporate in more sophisticated models to forecast sales?

The business owner is considering a massive social media push, and would like you to forecast sales if social media advertising increased to £3000. How would you advise the owner?

Question Four
In light of the Merchant City Redevelopment Strategy in Glasgow, the Scottish Government is offering two construction contracts. The first contract concerns the development of a "City Way" cycle network that will renovate and expand the existing one, while the second contract concerns the development of a Leisure Complex. SBS Constructions is a well-established company which is considering applying for one of these contracts.

In the case of the "City Way" cycle network, the company is considering the following three possible bid prices: £450,000, £470,000 and £500,000. Based on research in previous bids for similar projects, the estimated acceptance probabilities for each bid price are 0.75, 0.6 and
0.4 respectively.

The cost of the application for the City Way cycle network project is £22,000, while the cost of the design and the project plan which are required to be submitted with the application has been estimated to be £28,000. The labour and construction costs required to deliver a successful bid are £260,000.

In the case of the Leisure Complex project, the contract has a price of £8 million, with very specific design details and requirements. SBS Constructions is aware that 3 major companies have already applied an Expression of Interest (EoI). The preparation of the EoI has a cost of £35,000 and after the EoI stage, 2 companies will be short-listed. Each company has equal probabilities of being short-listed.

If SBS Constructions achieve to be short-listed, the company and its competitor will have to provide detailed designs that will cost £90,000. Each company has equal probabilities of being accepted for the contract priced at £8 million. Alternatively, SBS Constructions could make a better offer for the price of the project - £7 million - and increase its probability of being accepted for the contract by 40%.

The company estimates that it will be possible to deliver the project successfully by restricting the construction and labour costs to £4 million in total.

Construct a decision tree to represent the decision problem, including all of the relevant probabilities and outcomes.

Conduct analysis using your decision tree to explain what KMC Ltd should do. What is the expected consequence of your suggested course of action?

Question Five

JQ plc is a manufacturer of soft toys in the UK. They are interested in expanding their operations in Brazil, so they are investigating Brazilian companies with whom they can partner. They have identified four potential companies and six criteria on which they have assessed them to identify their most preferred. The six criteria are:
Interest: the extent to which the company is interested in working with JQ.
Technical: the technical challenges associated with working together.
Products: the potential synergies with the company with respect to their product range.
Growth: the potential to grow with the company.
Cost: the financial cost of working with the company.
Attitude: the level of professionalism within the company.

The value tree from the MCDA exercise is provided in Figure Q5a and the scores against each criteria are provided in Figure Q5c. Figures Q5b and Q5d provide other output from the V.I.S.A. software.

Which company is the most preferred? Please give a reason for your answer.

Which criterion is weighted with least importance? What is the overall weight?

Are there any dominated alternatives? Provide an explanation of what dominated alternative means and illustrate with reference to the data provided in Figure Q5c.

In Figure Q5d, the first plot shows the overall score for Nelly Furt decreasing, whilst the second plot shows it as increasing. Provide an explanation of what these plots provide to a decision maker and explain the reason for these changes in direction for Nelly Furt.

Attachment:- Mean and standard deviation.rar