While flu vaccination does not prevent COVID-19, flu vaccination is critical to protecting Australians' general health from influenza. A researcher surveyed a random sample of 62 people who had been given the flu vaccine last year and found that 21 did not contract the flu.

1. (1 mark) What is the proportion of people who did not contract the flu? (round to 3dp)
2. (1 mark) What is the lower bound of a95%confidence interval for the proportion of people who did not contract the flu? (round to 3dp)
3. (1 mark) What is the upper bound of a95%confidence interval for the proportion of people who did not contract the flu? (round to 3dp)
4. Using the confidence interval, can we make the following statement? The flu vaccine is effective (i.e.it prevents the flu) in50% of people vaccinated.

For Question 4 Answer using these three options:

• No, it is effective in less than 50% of people vaccinated
• No, it is effective in more than 50% of people vaccinated
• Yes, this statement is correct