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
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.
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
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