Moderna's COVID-19 vaccine was tested in 30,000 people. Half received the vaccine, and half received a placebo. Of the 95 cases of covid-19 that developed in the study, 90 were in the group that received the placebo and 5 in the group that received the vaccine. **For accuracy, please use 6 decimals for this problem in each step of your calculations.**

1. What proportion of the people who received the placebo became infected?
2. What proportion of the people who received Moderna's vaccine became infected?
3. If you want to test whether the proportions of infected persons in the placebo and vaccine groups are significantly different what is the appropriate type of test?
4. Carry out the test you selected in part C; assume =0.05.
5. Would you conclude that the proportions of infected persons in the placebo and vaccine groups are significantly different? Why?