What proportion of residents of New York City are vaccinated against covid-19? Because of double counting, lack of counting, poor procedures, lack of unified database, etc. it is not as easy a question as it might seem. However, NYC has an accurate database (Call it DB.) of all residents. (This is not actually true, but we will assume it.). Researchers at HJH took a random sample of n=4111 New York City residents from DB. Of these, x = 1871 residents were vaccinated against Covid-19. Let p be the (unknown) true proportion of New York City residents vaccinated against Covid-19. We want to estimate p. X is the random variable representing the number of sampled NYC residents who were vaccinated.

a) What type of probability distribution does X have?

Poisson

gamma

exponential

binomial

Weibull

b) What was the sample proportion,p, of sampled residents who were vaccinated?

c) What is the R formula for the expected value of X in terms of n and p?

sqrt(n*p*(1-p))

1/p

n*p*(1 - p)

n^2

n*p

d) What is the z critical value that we would use to construct a classical 91% confidence interval for p?

e) Construct a 91% classical confidence interval for p? (,

)

f) How long is the 91% classical confidence interval for p?

g) If we are creating a 91% classical confidence interval for p based upon the sample size of 4111, then what is the longest possible length of this interval?

h) Copy your R script for the above into the text box here.