Reference no: EM132855000

Keeping the border closed

Western Australia is a state that occupies the western 32.9% of the land area in Australia, excluding the external territories. It is estimated to have about 2.6 million inhabitants. The state is very cautious in protecting its residents from the transmission of the Covid-19 infection. Hence, it imposed a tough regulation to close its borders from other states which had recorded an increased number in Covid-19 infection. The residents however have mixed reactions to the regulation. Some were supportive to the regulation. Others argue that opening the state border should be made a priority to boost the economy. A survey on the matter is conducted over 3,000 randomly selected residents where they are asked to cast their vote ('SUPPORT' or 'NOT SUPPORT' on the decision to remain in closing the border). 1,680 respondents stated 'SUPPORT' for the state to remain closed.

a) Suppose you were a data analyst working for the State Office of Statistics. Assist the office in performing a hypothesis test at the 5% level of significance to infer whether more than 55% of Western Australian residents support for the state border to remain closed. Display the six-steps process (involving drawing the rejection region/s and determining the critical value/s for the decision rule) in performing the test.

b) Specify the decision rule to use in the p-value method hypothesis testing. Calculate the p-value of the test above. Display working.

c) Which one of these two types of error (i.e Type I or Type II) you could make with the conclusion you made in part a)? Briefly explain the reasoning for your selection.

d) What is the required condition for ensuring that the sampling distribution of the sample proportion is approximately normally distributed? Check if the condition is satisfied in the hypothesis testing that you just completed.