Refer to Exercise 12.54.

a. Find the margin of error for the estimate of the percentage.

b. Obtain a sample size that will ensure a margin of error of at most 5 percentage points for a 90% confidence interval without making a guess for the observed value of p̂.

c. Find a 90% confidence interval for p if, for a sample of the size determined in part (b), 28.8% of the sampled Malaysians infected with the Nipah virus die from encephalitis.

d. Find the margin of error for the estimate in part (c) and compare it to the margin of error specified in part (b).

e. Repeat parts (b)-(d) if you can reasonably presume that the percentage of sampled Malaysians infected with the Nipah virus who would die from encephalitis would be between 25% and 40%.

f. Compare the results you obtained in parts (b)-(d) with those obtained in part (e).