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.

a) The following data shows the number of hours slept by a patient in 1 weeks
12 18 09 16 11 10 08
i. Calculate the unbiased estimate for the population mean
ii. Calculate the unbiased estimate for the population standard deviation
iii. Calculate a 95% confidence interval for the mean number of hours