Epidemiologist: To successfully eradicate the Varia strain of the virus in the metropolitan area, at least 80 percent of the population must be vaccinated. The only currently approved vaccine, Novovax, requires two doses administered exactly three weeks apart to provide immunity. Public health records indicate that while 85 percent of the metropolitan population received the first dose of Novovax, a significant portion of those individuals never returned for the second dose. Consequently, the public health initiative to eradicate the Varia strain will fail.
Which of the following statements must be assumed in order for the epidemiologist's conclusion to be logically drawn? (Select all that apply.)
- AThe 85 percent of the metropolitan population who received the first dose of Novovax were uniformly distributed across all geographic districts within the metropolitan area.
- The portion of the metropolitan population that received the first dose of Novovax but failed to return for the second dose is greater than 5 percent of the total metropolitan population.Answer
- CIndividuals who fail to receive the second dose of the Novovax vaccine retain absolutely no partial biological resistance to the Varia strain.
- The metropolitan area will not achieve the 80 percent vaccination threshold required for eradication through the administration of a vaccine other than Novovax.Answer
- EEvery individual who successfully completes the two-dose Novovax regimen develops complete immunity to the Varia strain.
Answer
The correct statements are the one establishing that the dropout rate exceeds 5 percent of the total population, and the one establishing that no alternative vaccine will achieve the threshold.
For an assumption to be necessary, its logical negation must cause the argument's conclusion to collapse. Both correct statements pass this Negation Test. First, if the dropout portion were 5 percent or less of the total population, then at least 80 percent would have received both doses, fulfilling the threshold and destroying the conclusion that the initiative will fail. Second, if the 80 percent threshold were achieved through an alternative vaccine, the initiative would succeed, again destroying the conclusion. The argument strictly requires both of these unstated premises to hold true.
Step-by-Step Solution
Key Concept
Identifying multiple necessary assumptions in arguments involving mathematical thresholds and exclusive solutions.
Alternative Method
You can mathematically represent the total population as 100 people. First dose recipients = 85 people. Target required = 80 people. The maximum allowable drop-out to still reach the target is 5 people. Thus, the argument logically MUST assume the drop-out is greater than 5 people (5% of 100) in order to definitively conclude that the target of 80 will be missed.
Estimated Time:2m 30s