Question

Queensland is a state with a population of 5.1 million residents. It is reported that Queensland is doing very well in flattening the curve on the number of new cases of the Covid- 19 infection. Queenslanders are divided on whether or not the state to re-open for non- essential businesses. A survey is conducted over 1,500 residents where they are asked to cast their vote on the issue. 1,020 residents stated ‘yes’ for the state to re-open for non-essential businesses.

a) You were recently hired as a junior statistician working for the Office of the Premier of Queensland. Assist the office in performing a hypothesis test at the 1% level of significance to infer whether more than 65% of Queenslanders agree for the state to re-open for non-essential businesses. 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) Calculate the p-value of the test above. Display working. State the decision rule should you want to use the p-value method hypothesis testing.

c) This hypothesis test is conducted on the basis that the sampling distribution of the sample proportion is approximately normally distributed. Specify the required condition to ensure this. Further, check if the condition is satisfied.

d) Identify which one of these two types of error (Type I or Type II) you could make with the conclusion you made in part a). Briefly explain your selection.

Answer 1