Question: As everybody is focused on Covid-19 vaccines, you should note that no vaccine is \(100 \%\) effective. Some people are not protected after vaccination and for others the protection may wane over time which requires time series modeling. Generally, vaccine efficacy, measured as a percentage reduction of disease in a vaccinated group of people compared to an unvaccinated group, developed by Greenwood and Yule in 1915 for the cholera and typhoid vaccines, is still being used in practice.

To test the efficacy of flu vaccine used by GW Colonial Health Center during the fall of 2019 , a random set of 100 GWU students found that 40 of them had gotten a flu vaccine during the September of 2019. Of those who had a flu shot, 5 had flu during the winter. Of those who did not get a flu shot, 15 got the flu.

1. State your null and alternative hypotheses (2 pts)
2. Test your above hypothesis and state and support your conclusion \((10 \mathrm{pts})\). Use \(\alpha=0.05\). (you must show ALL your work)

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