Question

We want to examine the efficacy of the current flu vaccine at preventing the flu. Once flu season is over we ask 500 people if they got the vaccine and if they contracted the flu. We then break them into groups (those who got the vaccine and those who did not) and compare them based upon whether or not they contracted the flu.

Suppose your test statistic is statistically significant. Interpret what this significant result means in terms of the alpha and p-value AND what would you conclude about the null hypothesis for this particular research (retain or reject and state in words the conclusion you would draw about the relationship between the two variables).

Answer 1

We can have two binomial distribution with a total of 500 individuals where

Let '' denote the individuals who have gotten the vaccine and '' be those individuals who have contracted the flu.

Let '' denote the individuals who have not gotten the vaccine and '' be those individuals who have contracted the flu.

We are interested that in knowing whether the vaccine was effective that is whether the proportion of people who are vaccinated and did contract the flu is less than those who are not vaccinated and contracted the flu.

Therefore our hypothesis will be

( The proportion of people contracting the flu is same for vaccinated and non vaccinated people).

VS

( The proportion of people contracting the flu is less for vaccinated than non vaccinated people).

Test Statistic:

where Pooled variance =

If the test result is significant means

  p - value < (level of significance) and therefore We reject the null hypothesis.

Where p - value = the probability of the null hypothesis being true.

   is the level of acceptance of the null hypothesis. Since the p - value is less than , we can not accept null hypothesis since it is below the level of acceptance.

Conclusion: We reject the null hypothesis at and conclude that the proportion of vaccinated people contracting the disease was significantly less than those who were not vaccinated. That means the vaccine was efficient.