The prime Minister of a small Caribbean Island stated that 95% of the population was vaccinated from the Covid-19 virus. The opposition believes that the Minister is overstating the proportion of...

The prime Minister of a small Caribbean Island stated that 95% of the population was vaccinated from the Covid-19 virus. The opposition believes that the Minister is overstating the proportion of vaccinated citizens. He randomly selects 300 citizens and found that 240 of them were fully vaccinated.
i. Calculate a 99% confidence interval for the true proportion of all citizens who were vaccinated.
ii. Interpret you answer in i).
iii. State the null and alternative hypothesis of this test.
iv. Calculate the value of the test statistics.
v. At the 5% level of significance, determine if the Politian overstated the proportion of vaccinated citizen. Use the classical approach.