Question

The City Council of a regional area with a population of 15,240 people is committed to do a lockdown of the region if more than 3% of its population contracts the Covid-19 virus. To investigate whether more than 3% of the population have contracted the virus, the health

authority conducted a random Covid-19 test over 1000 people living in the region; 32 people tested positive to the virus.

a) You were recently hired as a junior statistician working for the Council. Assist the council in performing a hypothesis test at the 1% level of significance to address the problem specified. 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. 6 marks

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.

2 marks

c) Now that you have performed the test in part a), what would you suggest to the City Council, i.e. should the regional area be locked down? Yes or no? Why?1 mark

d) 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.

Answer 1

C) the region should not be under lock down because the virus contracted people are not more than 3% .

Answer - NO

d)

1) The sample are drawn by simple random method.

2) Sample size is no more than 10% of the population size.

3) let , np = 1000(0.032) =32

n(1-p ) = 1000*(1-0.32) = 968

So, both np and n(1-p) are atleast 10.