Among the 3,711 Diamond Princess passengers and crew, 712 had positive test results for COVID‑19 and nine tragically died as a result. Of those who tested positive, 331 were asymptomatic at the time of testing. Assuming that the passengers on the ship are a random sample from the population of people on the planet (they are not, because people who go on cruises tend to be older and more affluent than the general population), construct a 95% confidence interval for the proportion of people who test positive for COVID‑19 but have no symptoms. Because the number symptomatic and asymptomatic cases are both greater than 10, use large‑sample confidence interval. Give your answer in the form (lower, upper). Give the limits as a proportion, not a percentage, to at least four decimal places.
On January 20, 2020, the Diamond Princess cruise ship departed Yokohama, Japan, carrying 3711 passengers and crew. On January 25, a symptomatic passenger disembarked the ship in Hong Kong, where he tested positive for the SARS-CoV-2 virus, which causes a disease commonly known as COVID‑19.
On February 3, the ship returned to Japan, and on February 5, passengers were quarantined in their cabins. Initially, only those passengers with fever or respiratory symptoms were tested for COVID‑19, but later, testing was expanded to include older passengers, those with underlying medical conditions, and those in internal cabins with no access to the outdoors.
People who had negative test results or no respiratory symptoms, and no close contact with a person who had a confirmed case of COVID‑19, were allowed to disembark after being quarantined for 14 days.
Among the 3,711 Diamond Princess passengers and crew, 712 had positive test results for COVID‑19 and nine tragically died as a result.
Of those who tested positive, 331 were asymptomatic at the time of testing.
Assuming that the passengers on the ship are a random sample from the population of people on the planet (they are not, because people who go on cruises tend to be older and more affluent than the general population), construct a 95% confidence interval for the proportion of people who test positive for COVID‑19 but have no symptoms.
Because the number symptomatic and asymptomatic cases are both greater than 10, use large‑sample confidence interval. Give your answer in the form (lower, upper). Give the limits as a proportion, not a percentage, to at least four decimal places.
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