Question

A cruise ship was carrying 3,711 passengers on January 25th. A passenger showing symptoms of a virus departed the ship in Hong Kong and was tested for the virus. Testing confirmed he had the infection. On February 5th passengers were quarantined in their cabins on the ship. Ultimately 712 passengers tested positive for the virus and 8 passengers with the virus died.

Part 1: Identify the sample size, number of infections, infection rate, number of deaths, and death rate on the Cruise ship.

Part 2: Assuming the cruise ship is a subset of a population, use the cruise ship data to create a 95% Confidence Interval for the proportion of people you’d expect to contract the virus and for the proportion of people you’d expect to die from it.

Answer 1

Part-1:

In case of infection,

Sample size

Number of infections

Infection rate is given by

In case of death,

Sample size

Number of deaths

Death rate is given by

Part-2:

Corresponding statistic is given by

Infection proportion-

We know,

So, 95% confidence interval of proportion of people we would expect to contract the virus is .

Death proportion-

We know,

So, 95% confidence interval of proportion of people we would expect to die due to the virus is .