BUS105: There is a Virus Codenamed Covid-Pi Spreading Across the World It is Highly Contagious and Causes high Mortality Rates: (Online) Statistics Assignment, SUSS, Singapore

Background

There is a virus codenamed Covid-Pi spreading across the world. It is highly contagious and causes high mortality rates. A Multi-Ministry Taskforce is set up to tackle the Covid-Pi pandemic.

Question 1

(a) In order to decide the quarantine period for people who are at risk of having the Covid-Pi virus, the Taskforce must know the incubation period of the virus, i.e., how long it causes a person to show symptoms after he has contacted the virus. Worldwide Statistics shows that the incubation periods follow a Normal Distribution with a mean of 12 days and a standard deviation of 5 days.

(i) Find the incubation period that only 3% of the Covid-Pi virus will last beyond before showing symptoms in human bodies.

(ii) The Taskforce takes a sample of 15 airport arrival passengers who are tested positive for the Covid-Pi virus. Evaluate the probability that the mean of their virus incubation periods will be more than 10 days. Explain why this analysis can be conducted on small sample size.

Note: In Q(a)(i) & (ii), you shall use the relevant Statistics formula and Standard Normal Distribution table to derive the answers.

(b) The first vaccine that could fight the Covid-Pi virus was developed in February 2021 by Cosmos Pharmaceutical Limited (CPL). It is named the Conqueror. A sample of data was collected on its effective duration in weeks, i.e., how long the immunity lasts in a human body after the vaccination.

Six months later, another company Delta Life Science (DLS) develops its vaccine named Destroyer. A sample of data is collected. DLS Management claims that its Destroyer has a longer effective duration than Conqueror.

Note: Only one dose will be administered per person for either vaccine. The data is shown in the GBA Data file (see worksheet ‘Vaccine Effectiveness’).

Use Microsoft Excel to summarise separately the two (2) sets of data. Identify the locations and spreads of the samples, each with a measure that takes all data into consideration. Comment on their differences.

Present each data in an appropriate type of diagram. Comment on the data distributions.

(c) Use the Excel summary output in Q1(b) to identify the 95% Confidence Interval (CI) estimate of the mean effective duration for each type of vaccine, and interpret the confidence intervals. Hence infer any differences in the effective durations of the two vaccines.

State the requirement in using t-distributions to construct the confidence intervals. Justify whether this requirement is met in both cases.

Question 2

(a) Develop an appropriate Hypothesis Test at 0.10 significance level to validate DLS Management’s claim. You may adopt either a critical or p-value approach with the help of outputs from the Excel Data Analysis tool. However, you are required to show all the test steps.

Explain the type of Hypothesis Test Error that may occur in your test conclusion, the consequence of this error, and how the probability of its occurrence can be reduced.

(b) The Taskforce wants to know whether there are differences in various hospitals’ abilities to treat the Covid-Pi patients. It collected a sample each from a Public, Community and Private Hospital on their patients’ recovery periods in days as shown in the GBA Data file (see worksheet ‘Patient Recovery’).

Apply an appropriate test at 0.05 significant level using p-value approach with the outputs from Excel Data Analysis tool. You must show all the test steps.

(c) The Taskforce consults you on the approach used in Q1(b) and Q2(a). Discuss three (3) statistical concerns you have (excludes the issue on type of Test Error in Question 2(a)).

If you can start the process again from data collection to analysis, explain qualitatively how you would conduct the study.