Problem 5 (Hypothesis Testing for Population Proportion). Before a new drug enters the market, it needs to get approval by the Food and Drug Administration (FDA) to guarantee that it is safe. Only if a vaccine's benefits are found to outweigh its potential risks does the FDA grant a license for the vaccine, allowing it to be used by the public. The new vaccine Novatrax will get approved only if at most 5% of the patients will have side effects after taking it. The pharmaceutical lab that developed Novatrax claims that it meets this criterion. The FDA administered Novatrax to a test group of 1000 randomly selected patients, and found that 62 of them had side effects. Is this strong enough evidence for the FDA to deny approval of the vaccine?