Question

Recently, a health organization estimated that the flu vaccine was 65​% effective against the influenza B virus. An immunologist suspects that the current flu vaccine is less effective against this virus. Pick the correct pair of hypotheses the immunologist could use to test this claim.

Answer 1

The immunologist should use the null hypothesis (H0: ε ≥ 0.65) that the flu vaccine is at least 65% effective against the influenza B virus and an alternative hypothesis (H1: ε < 0.65) that the vaccine is less effective than 65%.

Step-by-step explanation:

The correct pair of hypotheses for testing whether the flu vaccine's effectiveness is less than the estimated 65% against the influenza B virus would include the null hypothesis (H0) and the alternative hypothesis (H1).

The null hypothesis generally represents the status quo or the claim that is initially assumed to be true, while the alternative hypothesis represents the new claim or the suspicion of the researcher that they are trying to find evidence for.

For this scenario, the hypotheses would be:

• H0: The effectiveness of the flu vaccine is at least 65% against the influenza B virus. (H0: ε ≥ 0.65)
• H1: The effectiveness of the flu vaccine is less than 65% against the influenza B virus. (H1: ε < 0.65)

In this case, the immunologist suspects that the flu vaccine effectiveness is lower than estimated, so he would be looking for statistical evidence to reject the null hypothesis in favor of the alternative that the vaccine effectiveness is indeed lower.