Is a flu shot really effective? In 2012-2013 the CDC reported that the flu vaccine was 56% effective. That is, 56% of all people receiving the flu vaccine who were exposed to a flu virus did not contract the flu. To check this claim (56% effective), a random sample of 50 at-risk people who received a flu shot was selected.
During the flu season, all 50 were exposed to the flu and 29 actually contracted the disease. Is there any evidence to suggest the claim is false, that the chance of contracting the flu is greater than 44%?