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.