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.

b) 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