- 2019 saw the first reported case of COVID-19. Scientists from the World Health Organization are tasked

with creating protocols for quarantining infected patients. In particular, they must outline the length of

time that patients are to be kept in quarantine before they are considered safe to release and no longer

contagious to the public.

Assume that it is known that the time to recovery has a mean of 14.36 days and variance of 6.82 days.

Be sure to define clearly any variables and models you use.

(a) Assuming that the time to recovery follows a Normal distribution, find the following:

i. An infected patient is selected at random. What is the minimum number of days that they

should be quarantined such that there is a 99.9% chance that they will be recovered before

release? [3 marks]

ii. 100 infected patients are selected at random. What is the probability that their mean time to

recovery is no more than 15 days? [3 marks]

iii. Suppose 21 patients on a cruise ship simultaneously and suddenly become infected with the

virus. With only 2 weeks remaining on their voyage, what is the probability that all patients

will be recovered before they return to port, as to not infect anybody on shore when they return

on the 15th day? Assume that the patients’ recovery are independent of one another. [4 marks]

(b) Assume the true distribution of time to recovery is unknown. Given this, consider the following:

i. Explain one reason why the Normal distribution might be a poor representation of the true

distribution of time to recovery? Briefly explain in 1 – 4 sentences. [2 marks]

ii. Is the probability you calculated in part (1(a)ii) still accurate? Briefly explain in 1 – 4 sentences.

[2 marks]

iii. A random sample of 144 infected patients reveals that their mean time to recovery is 15.09

days. Is the mean recovery time of these 144 patients unusual? Justify your answer using

probabilistic evidence. [2 marks] - Suppose a medical doctor suspects that 98% cases of COVID-19 would show fever symptoms. In order

to study whether fever is one of the most common characteristics of COVID-19, this doctor randomly

collected data on 1,099 patients with laboratory-confirmed COVID-19 and the result showed that 966

patients have experienced the fever.

(a) Use the doctors data to construct a 99% confidence interval for the true proportion of confirmed

COVID-19 patients who had fever. [3 marks]

1

(b) Write out the assumptions and conditions necessary for the interval you constructed in part 2a in

the context of the question. [3 marks]

(c) If we say “we are 99% confident the true proportion of confirmed COVID-19 patients who had fever

is between the range of the interval you calculated in part (2a)”. Provide an interpretation of that

sentence in the context of the question. [2 marks]

(d) When planning to estimate a population proportion, the doctor needs to determine the appropriate

sample size. Suppose the doctor doesn’t have any prior information about the proportion and

desires the estimate to be correct to within 0.05 with 99% confidence, how large a sample size is

needed? [3 marks] - A certain airline guarantees customers that the airline rarely loses passengers’ baggage. The public

relations department claims that on those occasions when luggage is lost, 92% is recovered and delivered

to its owner within 24 hours. An independent consumer group surveyed travelers on this airline and

found that 145 out of 165 people who lost luggage received their missing bags within 24 hours. You

will conduct a hypothesis test to see whether the data collected by the independent consumer group is

different from the airline’s claim.

(a) Identify the population of interest in the context of the question. [1 mark]

(b) State the null and alternative hypotheses in the context of the question in words. [1 mark]

(c) Determine/compute any conditions that must be valid to carry out the test in the context of the

question. [2 marks]

(d) Compute the test statistic. [2 marks]

(e) Find the exact value or provide a range of values for the P-value. Sketch your model, label and

shade the corresponding region (a sketch by hand is fine). [2 marks]

(f) State your conclusion in the context of the question with a 5% significance level. [1 mark]

(g) Based on your conclusion above, what type of error are you at risk of making? Explain your answer

in the context of this question in 1 – 4 sentences. [2 marks]

Sample Solution

hat there everything is predetermined and predestined to happen leaving no room for anything new to come into existence. Every action, thought or conscious decision that we make as a human is the effect of our previous action. In a greater sense, all events that have happened in history are effects of prior events. This leads one to believe that all things are concrete and unalterable in past, present or future. Determinism is a far reaching and radical notion that affects streaming beliefs such as morality, science and religion. Contemporary scientists have taken on the relative issue of human freedom by linking determinism and genetics through genetic determinism. This notion links determinism directly to DNA and the gene expression of a human. Gene determinism is supported by the idea that because of mishaps with certain genes it can lead to physical and mental alterations which means that we are physically determined by our genes. However, this is where genetic determinists want to expand on this idea and conclude that since we are physically determined by genes our behavior must also be determined by genes. This idea that our behavior is determined by our genetic makeup seems too radical and leaves no room freedom since we are genetically predetermined making us victims to our genetic makeup. Since science has the capability to alter genetics then that means they have the power to alter our physical determinations as well as our behavioral determinations. This knowledge of genes means we can alter ourselves and ultimately alter our behavior which will alter our morality. Although, if determination is true then human morality is merely an illusion because everything that happens would be considered a necessity. If all occurrences are set in time naturally without disturbances then there would be no room for immorality because morality would not exist. If we are predetermined to murder then it would be considered normal because it was aligned for us genetically and/or through our predestined behavior. This is where determination is faulty because it excludes all idea of freedom or choice. No one genetically wants to murder just as no one genetically wants to be murdered. According to a determinists it would be predetermined you would be a murder. However, this cannot be true because universally we have moral standards so therefore morality cannot be an illusion which eliminates the theory of genetic determination and determination as a whole.>

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