Question

An outbreak of a new virus has swept across a large city with over a million residents. City officials do not yet have the ability to conduct widespread testing of residents to determine the scope to which the virus has spread. In a random sample of 200 residents, city health officials find that 32 test positive for the virus.

a) In a random sample of 200 residents city health officials find that 32 test positive for the virus. Construct and interpret a 95% confidence interval for the proportion of all the city residents that would test positive for the virus at this point in time. (Show all necessary checks.)

Interval:.\

Interpretation:

b) (5pts) Does the confidence interval constructed in part (a) cover the value of the overall percentage of residents that would test positive for the virus? (Circle one)

Yes No Cannot tell

c) Suppose that the true overall percentage of residents that would test positive for the virus is 30%s. What percentage of samples of size 200 would produce an 80% confidence interval containing 30%?

d) What is the best way to decrease the width of a confidence interval without lowering the level of confidence? Write you answer using a single complete sentence.

e) City health officials currently believe that at least 15% of residents current would test positive for the virus. Determine the minimum sample size required if the officials wish to estimate the overall percentage of residents who would test positive for the virus to within 5% ounces with 99% confidence

Answer 1

We construct the C.I using the formula mentioned. The critical values are obtained from STATKEY (images attached for reference).